Hell YES.
Let's see. A few of my favourite Dark Sun characters (I mostly GM'ed, so these are all PCs run by other people).
* There was a defiler/fighter. He played around on some nasty adventures, before winding up with a slave tribe north of Nibenay. At first, he tried to use the Slave Tribe as a means of accomplishing his goals (the discovery of magical knowledge), but he found himself more and more interested in their lives. He kept his defiling secret from them, but eventually decided to get the tribe's preserver to help him "change" (he did this more from a practicality standpoint than out of any altruism). During one raid, he was nearly killed during a gith raid, when he got an obsidian scythe that sliced him from his buttocks up to his shoulderblade. He kept the scythe as a trophy weapon, and from then on when shirtless to show off the vicious scar. He sort of went a little crazy after that...
* An elven rogue who was far too larcenous for his own good. Several times he tried to steal money from the templars in Tyr (pre revolution). Or extort nobles for cash. Or just plain robbing merchants. Each time, his fellow adventurers did their best to distance themselves from him, knowing it was going to be his ruin. Each time, he got away (I was a lenient GM at the time, and he was a new player). Finally, he got caught, and was sold into slavery. His companions bought his freedom. Then, he stole again. His companions once more bought his freedom... and he robbed again. His companions (now having spent hundreds of ceramics on this damned thief) bought him again, only to keep him as a slave. When he stole a third time, again in Tyr, they let him rot away in the slave pens.
* A half-giant gladiator who was trying to make a living as a trader (his fellow PC was a human trader with a Mekillot that I don't quite remember). The half-giant had a pet kitten that he spoiled. He also had the Disintegrate psionic wild talent, which he would only use as a last resort in a fight (though it was nearly a guaranteed win). He once used his Disintegrate power on an enraged Mekillot, instantly destroying the beast's heart. However, since the half-giant was beneath the mekillot when the power was used, the half-giant was nearly killed. This was also the character who wound up fighting a kirre single-handedly in an "arena" in the halfling jungle... and was nearly killed (leading to the infamous "dice incident", in which an enrged player threw his d20 at my face and actually put a hole in my GM screen!).
* Jumai, one of the few Dark Sun PCs of my own. I don't remember Jumai's class, but I know it was some sort of warrior class. He was lightly armoured, and fought with a spear. And he had a pet monkey. Jumai wound up working on a silt barge, doing basic shipping work out of Draj and Balic while doing his best to evade giant patrols. Jumai met his end at the hands of raiders during a silt storm... he was trying to board the enemy barge and grabbed a loose rope to swing across - only to miss his landing. He fell into the silt, and suffocated.
* We had a half-elven templar from Nibenay (I think). His companions were a dwarven fighter and an archer of some sort. The templar did every sneaky, evil thing that templars are wont to do, all the while doing the work of his sorcerer king. his particular talent involved using his power to bully slaves and freemen into acting as his eyes and ears in his home city, although he got into more than a few political duels with other templar rivals. His companions (who were both good guys) had enough of the city life, and struck out for a ruin in the desert, dragging the templar along. I remember a few fights with undead in which the templar tried negotiation (and failed). Unfortunately, I remember this character more because his player wound up going crazy than out of the character itself (he was pretty standard PC, truth be told).
* In that same party, there was a dwarven fighter. His player was the guy who always played Dwarven Fighters, and thought Dark Sun was dumb because dwarves didn't have beards. Out of protest, he made his dwarf have a beard. I refused. So, there was a dwarven fighter on athas who actually made himself an artificial beard, and wore it around - getting strange looks from everyone. Other dwarves hated him, and most people thought that 'hairy dwarf' was not to be trusted. However, he was damned good with an axe, so his companions kept him around.
* I vaguely remember a human fighter who kept trying to be like a paladin. This never went well, and his morals constantly got him into trouble. He did all the wrong things - he trusted bards, he believed elves were telling the truth, and he instantly assumed preservers were "the good guys". Each time, he got burned... but he still stuck to his convictions, always believing in the best of people. He also saved up, and saved up, for a suit of plate mail. Yes... plate mail. Which made him the target of every thief, bandit, cuthroat, and raider out there. In fact, he was once on a journey to the southern "adventure city" of Celik when his transport was attacked solely for the purpose of getting his armour. HIs companions begged him to lose the armour, since he was causing so many problems ("if we sell it, we could all have metal weapons... and live like kings!"), but he stuck to his guns. His death was the part I remember most - on a road near the silt shore, his group was attacked by metal-hungry raiders. During the raid, some giants came across the battle, and fought both parties. Our metal-clad fighter was picked up and hurled into the silt by a giant. Everyone in the three-way melee that wasn't twelve feet tall mourned the loss.... of the armour.
* I dimly recall a mul gladiator who excelled in pit fighting (illegal, underground "fight clubs"). The only real thing I remember about him is his death. He died in a dungeon when he got trapped in a room by himself with a helmed construct that wielded a flaming sword. The Mul tried to pin the creature against the wall, immobilizing it long enough for his companions to break into the room and help him... only, he wasn't nearly strong enough. And the party's rogue wasn't nearly fast enough at breaking the locks.
***
As for PC types, we saw a lot of rogues in Dark Sun, as well as martial characters. Gladiators were particularly common. Clerics in Dark Sun were rare, though we saw a few earth clerics (I don't remember too many water clerics). Druids were a bit more common, but still were far from plentiful. I don't think I ever GMed a single psionicist. Mostly because none of us were really big on the psionics rules (wild talents were fun, though).