How do the various Borderlands 2 characters complement certain playstyles?
This isn't anything like the stupid restrictive classes in Mass Effect - they're not limiting like that. Anyone can be pretty devastating with any gun, but the skills are awesomeness on top.
Each of the characters has three branches to the skill trees, which seem to always be of roughly the same types:
The left branch offers some good early bonuses and is easy (or at least obvious how) to master. For instance Maya gets more shields and gun damage, Zero gets more sniper damage.
The middle branch benefits co-up (healing your teammates, allowing them to do more damage, etc). For instance Maya gets team healing, Zero can tag enemies to do them more damage.
The right branch is tougher to master but offers some serious klout at the top. For instance Maya gets more elemental damage (useless until about level 15 when elemental guns start to be plentiful enough, but devastating at level 50) and Zero gets insane melee damage and re-cloaks with melee kills.
Respecs are cheap and respec stations in the hub areas of the main game and DLC, so you can tweak your characters a lot. At level 5-20 you find yourself on the left a lot, but the real fun comes with lots of playing around and respecs later on.
The massive differences come at higher levels, and it really becomes about using the right weapons for the playing style.
You can focus on DPS for any of the characters, but it will work in different ways: Maya gets per-shot elemental bonuses (making SMGs/Shotguns do insane damage) while Salavdor gets never reloading and ammo regen (making Vladof spin-up assult rifles devastating) and so on.
All the high level powers are pretty cool.
Axton is the easiest to master and the most conventional - he's a lot like Roland in BL1. His turrets get pretty awesome and it's essential to have at least one Axton on your team for kiting some of the level 50 boss raids.
Salvador is the next easiest: he's all about spitting loads of ammo but he can also become pretty tank-y. He can keep spewing lead even when fighting for his life which can be a good survival tactic.
Zero can be either sniper or melee, you kind of have to pick one or the other. I found levels 1-20 as a sniper and then 20+ ninja everything :-) With the right gun and an Amp shield Zero can take down or nearly wipe out most enemies in a single head shot.
Maya is all about elemental damage - if you understand how to use that, what enemies are weak to it, which ones resist it and how it stacks then she does (by far) the highest DPS, possibly even overpowered. It can take some getting used to, and you find that you need one of each elemental weapon type to hand all the time. Maya is also essential for some co-op with her healing tree and is the only character that can remote-heal others.
I'm not that used to Gaige yet, but I think her skill (by default) is a little like Axton's - the real fun is in her 'right' tree: Anarchy. By changing the reload dynamic it makes it tough to master (you'll swear because you accidentally hit reload instead of open chest because you were slightly too far away).
In short: whoever you pick you'll find something to enjoy in the playing style.