Generally enhanced physiology
Spider-Man's overall metabolic efficiency has been greatly increased, and the composition of his skeleton, connective tissues, muscles, and nervous system have all been enhanced. Originally, Peter Parker wore glasses, but after the awakening of his mutant powers, his vision became 20/10 at the cost of being permanently changed, allowing him to see perfectly after his spectacles were broken by the push into the street. He is capable of healing injuries faster and more extensively than ordinary humans, including injuries as severe as SET broken bones within a matter of hours. During a battle with a villain he was rendered completely blind. However, during a visit to an eye specialist, it is revealed that he was already healing only hours later. After about two days, Spider-Man's 20/10 vision is restored, although his eyes are sensitive for about a day after, shown when a camera flashed a bright light in his face. Afterwards, his eyes are completely healed. However, Spider-Man's healing factor has not been depicted as being anywhere near as rapid as that of Wolverine or The Hulk, in as much as he has suffered life-threatening injuries that would not have endangered those other superhumans.
His accelerated metabolism increases his tolerance to drugs, meaning a larger dose is needed to cause the usual effect, and he can recover from the effects rapidly. During an encounter at a bee farm Spider-Man is incapacitated by thousands of bee stings, but fully recovers in less than 24 hours. His resistance to other toxins varies, but is typically significantly higher than normal. However, he has normal human tolerance to the effects of alcoholic beverages and is rarely shown drinking, since it affects his balance, reflexes and coordination. In one battle, he nearly loses his life after unknowingly consuming spiked punch at a party. Although he is still affected by disease and infection, his recovery time is typically shorter than that of an ordinary human. His unique physiology could even allow him to recover from the effects of vampirism.
Spider-Man is still vulnerable to disease and has fallen ill due to flu many times; which affects the reliability of his powers. He also has certain susceptibility towards ethyl chloride, which is a commonly used pesticide against insects and arachnids.

Wall-crawling
Spider-Man is capable of crawling on walls and ceilings. He has conscious control over this ability, and it is simple and instinctive for him to use. Originally, Spider-Man is able to stick to surfaces using only his hands and feet, but with training he is shown to be able to cling with his back. The strength of attraction between himself and the surface he is clinging to is considerable, with an upper limit of several tons per finger. If Spider-Man does not willingly detach, but is pulled off by force, the surface usually breaks, still attached to his body. However, it has been shown that a significant shock can cause him to lose control of his power and fall off a surface. If a surface is too slippery, he has problems sticking to it; if it is too fragile or crumbling, it is unable to support his weight. He can also use his clinging ability to lift or hold objects; for instance, he can catch a thrown ball simply by touching it with one fingertip. Spider-Man is also able to jump and sprint against a wall which helps him climb surfaces a lot faster.
The ability works through thin layers of cloth, such as the fabric of his costume, but not through materials such as the soles of shoes. When he needs to crawl without changing into the costume, he removes his shoes first.

Enhanced strength and durability
Early in his career, Spider-Man was frequently said to have the proportional strength of a spider, but he can lift much more due to his human size and physical build, up to 10 tons. He has been shown to lift and throw objects such as a tank and a semi-truck and to bend the steel of a screwdriver with one finger with ease. When in combat, Spider-Man must pull his punches unless fighting someone of similar or greater durability and power. Otherwise, his blows would kill a normal person.
Spider-Man's bodily tissue is a great deal more durable and resistant to some types of injury than a normal human (for example, a regular villain punched Spider-Man and broke his wrist). However, Spider-Man is far from invulnerable. While his body is tougher than an ordinary human, he can still be injured in ways comparable to an ordinary human. For example, Spider-Man can be injured by bullets or knives composed of conventional material and from impacts of sufficient force. However, if injured, his accelerated metabolism is capable of repairing itself many times faster than an ordinary human. A doctor has told Spider-Man that it would be impossible for a normal man to survive the punishment that he has endured.
Spider-Man can leap several stories vertically or the width of a city street. While his running speed has never been definitely established, he can run at superhuman speed for short sprints and has been shown to be easily capable of overtaking fast-moving cars, but nearly always prefers using his weblines to travel.

Spider sense
Spider-Man's "spider-sense" manifests in a tingling feeling at the base of his skull, alerting him to personal danger in proportion to the severity of that danger. For instance, a little tingling such as a happenstance passing by of an enemy would prompt Peter to be alert, while a strong tingling, sometimes to the point of being painful, is interpreted as a need to take immediate evasive action on a deadly threat. It appears to be a simultaneous, seemingly clairvoyant response to a wide variety of phenomena. Though the exact mechanism of this ability is unknown, his spider-sense clearly has at least two aspects in addition to sensing potential or immediate danger:
A psychological awareness of his surroundings, similar to the radar-sense of Daredevil. When he is temporarily blinded, he can emulate this ability and navigate without his eyesight. Even under normal conditions, his spider-sense helps him navigate supernaturally darkened rooms or places with strobing light, instinctively avoiding obstacles or hazards, or potentially noisy or unstable floorboards, walls or ceilings that may betray his presence.
Using his spider-sense to time his enhanced reflexes, Spider-Man can casually dodge attacks up to and including automatic-weapons fire. Even point blank, his spider-sense has already warned him in enough time to get away like a precognitive sense, before he can even consciously think about his actions. However, he can ignore this instinct. His spider-sense is sufficiently well-linked to his reflexes, that a threat can trigger them even when Spider-Man is asleep or stunned but not outright unconscious.
When Spider-Man swings across a city on his weblines, his spider-sense guides his aim, allowing him to travel at high speeds hundreds of feet above street level with minimal concentration, confident his weblines will find secure anchor points.
Spider-Man's spider-sense is directional and can guide him to or away from hidden weapons and disguised enemies. Sudden and extreme threats can cause his spider-sense to react with painful intensity.
Spider-Man can also sense and dodge attacks directed randomly or by a computer. His spider-sense has helped him preserve his secret identity since it alerts him to observers or cameras when changing into or out of his costume. The spider-sense does not react to those whom Peter does not consider a threat, such as Aunt May. Contrary to this, his spider-sense has warned him of people close to him when he does not wish to be seen, such as when he's partly in costume.
Spider-Man can choose to ignore his spider-sense, and distraction or fatigue can force unawareness. Broad spectrum radio transmitters that fire on all frequencies create fog/static/white noise that can impair his ability to react to unknown dangers.

Sense perceptions
Spider-Man's five primary senses are above average perception, though not superhuman, as a result of his spider powers. He can feel vibrations and currents in the air or in his web lines, much like a real spider.

Arthropod communication
He can mentally communicate with arthropods (at least insects and spiders), though he does not seem to be capable of controlling them like Ant-Man. He can sense their presence, or glance at any spider and instantly know what kind it is. It is possible that this is an extension of his spider-sense.

Biological webbing
At the onset of his mutations as a teenager, he developed the ability to shoot organic webbing from his wrists. it possesses an amazing tensile strength equivalent to 120 lb (54 kg) per square millimeter in cross-section and is comparable to nylon with extraordinary adhesive properties. Its exact composition is unknown, but after about an hour, the webbing breaks down, loses strength and eventually evaporates. In order to replace the lost nutrients from the web expulsion, he consumes nearly one hundred times the protein of an average human (5000 grams) Which averages to ten pounds of protein daily. (An average spider produces 65 yards of silk a day. The largest spider by weight is 6oz, Pietro is 440 times the weight of the largest spider, 440 X 65= 28,600 Yards of silk a day or an average of 1200 yards of silk an hour)

Arachnid physiology
His eyes are naturally all red and take up the entirety of his eye socket rather than pupil/iris/sclera, these mutated eyes provide him with night vision. The stingers are made of keratin rather than bone within his forearms and protrude from over the top of his wrists when he extends them (like baraka from mortal Kombat). The stinger only extends as long as his middle finger across the back of his hand to prevent from overextending and being broken off but grow back as fast as nails or hair if it does happen, this couples with his healing factor tends to mean by the next day. They are coated in a neurotoxic venom that inflicts temporary paralysis, though the impalement itself can prove fatal. If you have a central nervous system, you are capable of being subject to the venom.

Superhuman reflexes and agility
Spider-Man's agility and reflexes are far superior to those of an ordinary human, even those that represent the peak of human conditioning such as Captain America. The speed of his reflexes combined with his spider-sense allows him to dodge almost any attack, even gunfire at point blank.
Spider-Man has the ability to maintain his equilibrium on any surface that he can stick to. For example, he can balance on one finger on a high wire, or stand upright on a wall, his body parallel to the ground. Additionally, he is able to flex his body like a contortionist, assuming postures that would be impossible or harmful for most normal humans. His tendons and connective tissues are at least twice as elastic as the average human being's. This ability is often demonstrated by the unusual poses Spider-Man would assume while webslinging or dodging enemy attacks. Also, as an outcome of his spider-reflexes, Peter has developed his own fighting style.

Not to rely solely on his mutant powers, he also has been building on his genius intellect to not only create his own devices but to reverse engineer or incorporate defeated villains equipment into his own gear as well, rather than turn them over to the police.

Mechanical Web-Shooters:
In addition to his own standard organic webbing, he has been experimenting with the potential of his own webbing for decades. When not in costume, he wears harvesting devices on his forearms that collect his web fluid and paralytic toxin in a nitrogen filled 'vacuum' to prevent oxygenation. When in costume, he keeps a supply of webbing with a mechanical release either for when his own glands run out or to make use of specialty webbing as the situation demands.
Each cartridge is comparable to a standard 12 gram Co2 capsule and contains 6 liters of fluid stretched and woven into roughly 6000 feet of 1/4" webbing (about 600 ten foot 'shots' or 60 hundred foot "swings").
Each cartridge takes 5 hours of no incident to harvest, 4 capsules a day, 5 a day of high food intake.

Some of these modifications include:
*Non-conductive webbing (typically for dealing with electrical opponents or loose wire/3rd rail threats),
*Flame-retardant webbing (against Fire-based opponents or out-of-control fires),
*Stronger (yet much less stable) webbing for dealing with super-strong enemies, It lasts 60 seconds instead of 60 minutes
*Acid webbing that can eat through tough organic tissue like other physically super durable mutants.
*Highly conductive webs to use electrical currents like a taser and make an electrified web.
*Flash webs that ignite like a road flare after exposure to air for a few seconds to blind the enemy
*Magnetic webbing, which is used to interfere or cancel out radio or remote-control frequencies.

In addition, he has harvested his paralytic venom and set them to small injection darts he can fire with the same accuracy as his web shooters.

His costume itself is a weaving of his webbing with specific controlled exposures in order to not only prevent the breakdown, but also leave him with a bulletproof and non-conductive body armor. This time consuming process is one that can only be performed in lab conditions and so is not common for him to whip up a new suit on the fly. He has also taken the time to make a fire-proof suit as well, but keeps that to the side as a known situational occurrence.

Spider-tracers:
After too many villains getting away, he came up with small electronic "spider-tracers" of his own design that allow him to track objects or individuals. Typically, he plants one on a departing enemy, or throws one to adhere to an escaping enemy and then follows the target to their hideout for later attack. Spider-Man sometimes also uses a launching device in his web-shooters for better range and accuracy.
A tracer's outer casing is shaped like a spider, with legs for aerodynamic flight with listening devices to broadcast to a reciever for evidence collection and GPS. The tracers are small enough to remain unnoticed, in general, but sometimes a target finds a tracer and destroys it. Currently he uses a small electronic receiver to follow the signals of his tracers rather than cue it to his spider sense as he does not want it to interfere as 'white noise' in a dangerous situation.

Utility belt and Camera
In combat he keeps his regular field equipment in a utility belt that can carry extra web fluid cartridges, spider-tracers, and his camera. The belt can hold up to 30 cartridges, each one being pressured to 300 psi. The belt's buckle contains a small but powerful light, which is filtered through a lens decorated with a stylized likeness of Spider-Man's mask and has a UV light setting for forensic analysis(and vampires). This spider-signal is mostly limited to intimidating weak-nerved criminals and acting as a wide-beam flashlight, it is sometimes used to call for help as well or leave a marker behind if he has to scout ahead.

Web Grenade(player invention)
26 web cartridges arranged in 45 degree increments in a radial sphere releasing 156 liters of web fluid in every direction. This is another one of those resource consuming devices due to the number of cartridges needed (it takes 1 week worth of webbing for enough cartridges to make each grenade.)

Acquired tech
After recently defeating shocker, he is currently exploring how to introduce this new tech into the next suit design. This might be where he actually introduces a web pattern into the costume to replicate the shockers suit ability to disperse the backlashed energy.