While not an ‘RPG’ in a sense, Planetside had this really neat bug that used to happen. If you were defending a base, and there were LOTS of enemies outside, sometimes most of the the indoor textures would suddenly turn black. In-game, this really reminded me of a blackout. It wasn’t intended, but gave a really cool effect to the atmosphere at the time, particularly during raging shootouts when everybody suddenly can’t be seen, except for certain particle effects (projectiles, muzzle flashes, glowy weapons, etc)
In an old M.U.D. I used to play years ago, the Steal command could actually be used by anyone; it simply was that ordinarily your chance of not getting caught was zero if you weren’t a Thief who had been able to practice Stealing inside the Thieves Guild. HOWEVER: characters that were under a spell of Sleep could not awaken unless attacked, and they forgot to make unsucessful attempts at Stealing to count as attacks. So if you could get a Sleep potion and use it on a filthy rich character, you could rob them blind. I was soon able to afford incredibly expensive equipment for my character level.
A couple from WoW.
I was questing in the western plaguelands and tried to attack a searing ghoul. I immediately noticed two things.
-His life wasn’t going down
-My spells were firing upwards
Tilt the view…yup, there he is about 30 feet above the ground, just standing on thin air. I guess it’s another form of the floating corpse bug which seems to be running a bit rampant right now 
This one happened a lot early on in open beta, and I’ve seen it happen at least once since then (not to me though). For those who don’t know, players can take griffons to fly from place to place. While you’re on the griffon all you can do is sit back and enjoy the view. But at the time, often the player would be given control of the griffon and instead of following the predetermined path, you could control where it went. The inside of the nearest inn seemed to be a popular place to fly, although one of my friends also enjoyed going underwater with it.
There’s an occasional bug in City of Heroes that causes invisible mobs. Suddenly everything in melee range disappears except for their weapons and attack effects.
More common are the mobs that don’t fall over when they’ve been defeated.
One rather silly bug in the Realm, an old Sierra MMORPG, was the fact that one could buy or sell negative quantities of something, and it would go through.
Needless to say, this created rather interesting side-effects.
In EQ, there were several. Pathing “exploits” and such, too numerous to go into detail. But one I remember quite fondly. Was running around with my 30 ranger in West Karana right after the servers came up. Starting killing things and found out that I was losing any health. Figured it was just a graphic bug, since I was getting text that I was indeed getting hit for damage. Happened to see a Hill Giant on track and decided to test it out for sure. This was prekunark. Only the uberest players were able to solo HGs. Sure enough, I couldnt be killed. But the problem was I was barely hitting him. 15 mins into the fight, the servers were brought done and then there was no more fun. I’m guessing I wasn’t the only one who found out they were immortal that day.
I’ve seen it happen several times (and I started playing well after beta). There was one post on [url=www.livejournal.com/communities/worldofwarcraft] where photos were posted. The person it happened to visited Sylvannas and her pet demon lord, then decided to see if the effect would carry over if he took the zep to Orgrimmar.
It didn’t. A zep full of Horde made quick work of his poor little Nelf toon…
A well written description of a dupe bug in EQ2 that earned the perpetrator “more than some people make in a year…hell…maybe 3 years, and it was enough to take my girlfriend and entire family on a vacation to Paris.”
I once saw a couple of Freeport guards in Everquest ‘overlapping’ each other in a way that their idle movements made it look like one guard was pleasuring the other. Yes, nerd that I am, I have screenshots 
I have screenshots of that, too! I must be a pretty big nerd myself, because I just went looking for them - but didn’t find them. I did, however, manage to dig up my old buddy Krak in South Karana with one of his gimps (check it out, that’s me in the background - haven’t seen her in so long I forgot what she looked like).
My favourite bug was when this started happening everywhere… and as quickly as they came, they disappeared with no explanation.
This is one of my favourite screenshots of when mobs would die but not hit the ground (ouch!)
But this… this… it’s not a bug, just a trick of the eye. Hey, banker, how you doin’?
I don’t have as many cool screenshots of EQII… yet.
I like holes in the world–you know, gaps in the geometry where you can get outside the game space. A few turn up in City of Heroes whenever a new zone goes live. Of course, if you can’t fly, you usually just fall through and get respawned in a random location. If you can fly, however, you can explore. It’s fun looking at all the bits of geometry that stick out, and given that CoH allows you to target things from outside (but not vice versa), you can annoy mobs with impunity or deliver buffs and heals from nowhere on people. Regrettably, that makes it highly exploitable, so I bug them when I find them.
Another fun one in CoH is a rare mission glitch that dumps you into someone else’s ongoing mission when you try to enter your own. My level-capped defender got dumped into a lowbie’s mission once, much to his shock.
“Who are you?!”
“I’m God Mode.” <buff-buff-buff-buff-buff-buff>
Something similar happened to me on the test server recently. My level 8 blaster died on the way back from a mission, and, as customary, was teleported to the hospital. The thing is, you’re supposed to go go the hospital of whatever zone you were in last.
I ended up in the newbie tutorial.
To make matters worse, it appeared to be an ‘instanced’ newbie tutorial that I was the only one in!
Soooo… after getting my isolator badge (for defeating x number of newb mobs) I decided to unleash on some of the ‘unkillable’ practice drones. Turns out they really are unkillable, no matter what level you are.
Finally petitioned my way out. The GM involved seemed rather distraught that this bug had started showing up.
i remeber in EQ sometimes in misty thicket id see 2 rats stuck together in some sort ofspawning bug.
2 headed Rat!
Gliven.
I had to commit suicide with my already dead Undead by throwing myself into the nearest body of water and drowning in WoW.
That wasn’t cool, though.
Wow! That was really interesting - thanks for the link!
George
I thought undead had Underwater Breathing - unable to drown… I may be wrong, of course
George
So that’s why every damn thing on the broker cost so much. That’s not a cool bug at all. 
Yes, we do. What I’m talking about it’s a bug. You’re dead but with your life bar filled. You have no corpse and the angel doesn’t appear. The only way to fix this is to drown yourself.
I thought they removed that after beta and gave undead 3x the regular breath bar instead.
Couple more not so cool ones–
This has happened in WoW, and unfortunately to me. There were a few places where the mage spell Blink could send you under the world. The fall is an instant-kill. ( though if it ever happens again I want to see if a barrier will keep me alive).
Occasionally, the boat ride will drop everyone riding the boat when it hits the edge of the zone. Which royally sucks because I don’t think even paladins can manage to make it back to shallow water before the fatigue bar kills you.
That reminds me, a server glitch once placed one of my Heroes under the landscape while logging in.
Unending breath is a racial spell that you have to cast. It lets you breath underwater for, um, half hour? Hour? A real long time.