The weaknesses of vampires depends upon their bloodline. The different bloodlines function slightly differently.
Dracula's Bloodline is the most common. They are vulnerable to crosses, holy water, stakes to the heart and beheading. Burning them to a crisp will also kill them. Garlic and the like will do nothing to them. They rapidly regenerate damage and have a poison resistance far beyond that of humans, but they can still be put down by these things. Pretty much all vampires fall under this category, and as such you can generally assume this shit works.
Then there are the truly old vampires, Gods. They are so ancient, they were revered as deities by ancient civilizations. Most of them can only be harmed by symbols specific to their own religion, bound by special rituals to their religion, etc. To take on one of these vampires without having specifically researched their weaknesses is folly, and will get you killed. Almost all vampires older than Dracula are biologically dead, and as such unaffected by poison and suffocation.
There is also the bloodline of the Pale Lady, which stems from the Lady of the Lake in Arthurian Myth. These vampires are able to exert some form of control over their spawn, although the extent to which these functions depends on the vampire. Only Bedhivere and his lackeys are a part of this bloodline (as well as, obviously, the Pale Lady.) For more information on these mysterious vamps, you're going to have to go to Bedhivere.
Small database of vampires and weaknesses:
Magnus
A Draculan oldblood, although Magnus has removed his heart from his body and replaced it with a machine. This means that stakes will not harm him, unless you manage to find his original heart. Like many Draculan vampires, he has mild psychic capabilities. This means he is able to influence his opponents, creating mild illusions and performing acts such as Telepathy.
Bedhivere
As aforementioned, Bedhivere is the spawn of the Pale Lady. During the night, he is one of the most powerful vampires ever to walk the face of the earth, in sheer power he becomes unmatchable. During the day, however, he is no more powerful than a normal human, and as such if you catch him at this time he is easy to kill. Christian symbols will affect him, I'm unsure as to whether he is biologically alive or dead.
Gabriel
Thought to be one of the oldest vampires alive, Gabriel is his own bloodline. He is biologically dead, and far older than Christianity. He cannot be harmed by Christian symbols, and those of his bloodline must be killed through decapitation or a stake to the heart. Whilst he is physically unimpressive, he boasts the greatest psychic capabilities of all vampires. He is able to completely dominate lesser foes, shaping their perception of reality to his will. Throughout the entire history of the human race, nobody has managed to come even close to killing Gabriel, giving him his legendary status.
Lady Mo
A God vampire, Lady Mo is an ancient North American nature spirit. She is not harmed by Christian symbols, and can only be harmed by the ancient rituals used to bind and kill such spirits. Decapitating her will most likely also kill her, although up to this point nobody has been able to test this. She can transform into animals, dominate the weather, and exerts immense physical capabilities. She controls nature as her battlefield, and is most deadly when faced in the wild.
Several other ancient and powerful vampires exist not yet incorporated into this database, but most fall into one of the Bloodlines described above and should be killable through such methods. As the story progresses, new bloodlines may appear, either old or new. A new Bloodline is formed when the traits a vampire bestows upon it's kin vary so greatly from the original that it's a new 'type'. And, of course, if it grows big enough for anyone to give a shit.