I've re-used most of my characters in some way, shape, or form. Although none of them are a 'main' simply because my RPs span so many different genre none of them are one-size-fits-all...
yet.
Sometimes I just allude to some old half-forgotten RP for old time's sake, sometimes they lift their backstories directly from a previous RP.
With a character like that, at least for myself, I feel drastically more connected to them. Like they're alive in a way. This sort of thing is only possible after a set amount of time, I believe. Well, at least for me. I can't rightly speak on how it is for others. I think it's also important to note that a majority of the games that I've participated from the start have been largely war and battle-oriented. A persistent character jumping from one battle to the next is eminently more "experienced", which confers an extra advantage to the player as time goes on (I know there are likely folks who would disagree with this for whatever reason, but that's a whole different discussion).
That.. at least for me, is a different can 'o worms.
When a character becomes persistant, their motives quickly become a complicated tangled hot-mess, but nevertheless, the characters are often highly motivated in whatever they do, and believably-so;
no matter how ridiculous their story may sound.And every so often, I run into a quirk of characters not only getting more skilled than the myself the writer, but also managing to see plot-events coming, prepare for them on their own,
and actually outsmart the writers... Or rather, just posting what the character would do normally, and find out in OOC chatter that I somehow had my character outsmart some other character when in the meta of OOC I was outsmarted/fooled by the other writer.
But that has more to do with how I work on writing a post than character-persistance (well, aside from granting them an independent train of thought and letting that run for a few years without me). And how that jives with the more traditional writing-style of people I RP with.
It doesn't really give them a direct advantage, but
usually they end up befriending other persistant characters, which usually means a whole can of spec-ops hurt is just one seemingly random phone-call away.
Which may or may-not involve a phone-book and a baseball-bat IRL.