In Operation Flashpoint you don’t have to restart the game from the beginning, you just have to retry the mission. There’s no penalty for doing so.
I just remembered a funny one that someone posted in a similar thread a couple years back.
It was in the original Half-Life. There’s a scripted scene where one of the professors falls to his death in an elevator shaft; he falls right past your character, Gordon Freeman. However, there’s also some kind of AI trigger whereby when the professors see you, they greet you with a friendly “hello, Gordon!” The net result is -
“Aaaaarghhhhhh<normal voice>Hello Gordon<>aaaaarghhhhhh!”
Battlefield, single player: run to the other side of the map and commandeer the opposition’s tanks. Blowing up the AI with its own tank is fun while it’s trying to figure out what the hell is going on!
City of Heroes has a “I’ve fallen and I can’t get up!” cop in The Hollows near the Atlas Park gate. He repeatedly goes between sitting and trying to get up; sorta looks like he’s breakdancing. He’s behind one of the sandbag walls north of Wincott.
In Battlefield 2, if the server dies (not if you lock up–your version of the game has to be happy for this to work), your client remembers which direction all the vehicles were going and has them continue on in a straight line… including floating through the air, tumbling slowly end-over end… kind of funny seeing a tank drift slowly across the interesection.
Another cool thing in the original Half-Life which just seems realistic and not a glitch…
if you can shoot a soilder just as he’s about to throw a grenade, he’ll drop it and blow up his buddies. I don’t know why, but the first time it happened I thought it was the coolest thing ever.
Reminds me of something – in some football season simulator (1998 edition, I forget which franchise,) the referee went out on the field to announce penalties, and at the end of course said something like “First Down”.
However, there was a lag between these two words, which made it come out like
“First ------- Down.” Which sounded like they bleeped out a word.
Speaking of breakdancing, I give you one of the guards from “Far Cry”.
I’ve found some good ones in Oblivion. One of the cool things about the game is that the NPCs wandering around town will start random conversations with eachother. Sometimes, these conversations will reference other things you’ve done in the game, or information about things going on outside town. One town is having problems with Goblins in the surrounding wilderness. Apparently, it’s a very popualr topic, because I walked into the tavern and heard three different people say, in unison, “I hear there’s been a lot of Goblin activity outside of town!” And three responses, in unison, of “Goblins, huh? Sounds dangerous!” The whole conversation went like that.
Unlike a lot of other RPGs, people get really pissed at you if you just wander into their house. It also has a system where it grabs random snatches of conversation whenever you stand near an NPC, depending on how that NPC feels about you and where you’ve encountered them. Going into someone’s home univited usually gets you yelled at. In one case, I had just completed a mission for a woman, rescuing her husband from a bunch of trolls. We’re standing in her living room, and she says something like, “Thank you for saving him! You’ll always be welcome in our home.” The scripted conversation ends, and suddenly she shrieks, “Get the hell out of my house!” That’s hospitality for you!
That was actually the beauty of OFP–just how organic the game was at times. Sure, you’d have to retry the mission, but it makes for a good story. 
My favorite experience with OFP happened when I finally beat this insanely difficult mission early on that had me stuck. You’re out on a mission with your buddies and they leave you behind enemy lines. Every commie on the island is now beating the underbrush for you and you have to get back to a rendezvous point a mile or two away.
So, I sneak through a pine forest, hiding from patrols and the chopper they have searching for me…see a village with vehicles in it in the distance. Throwing caution to the wind, I make a mad dash for a small blue car. Just as I hop in the car, I hear a boom–the enemy must have radioed in for a tank or something. So, I go speed off down the road, swerving like mad to avoid incoming fire.
About a quarter of the mile from my destination, the tank finally gets me. The car explodes, throwing me in the ditch. When I stop bouncing, I try to stand up. Screen turns red, my character makes a muffled “URRRGHHH” noise and falls down. Turns out, the tank blew off my legs, but I’m still conscious. Okay, so I crawl the last couple hundred feet to the rendezvous point and complete the mission. Barely.
My favorite part about this is that the next mission automatically starts you in a tent about to be ambushed by the enemy. In a standing position. Without healing you first.
So, the first thing that happens is…“WE’RE UNDER ATTACK!!!” gunfire Then I instantly scream like a little girl and fall down.
Fortunately, they heal you after that mission…no idea how I managed to get through it…
One of my funniest moments in Half-Life took advantage of the “tossed box” glitch.
Any object that could be slid or pushed across the floor would be tossed up if it encounterd a slanted surface that gave it a ramp to jump. The behavior of tossed objects was highly unpredictable but in general they would take off flying impossibly high, and if they were still on a slant like the 45-degree lift shafts they would continue to slowly climb almost indefinitely.
Anyway one of the repercussions of this is that in a few places you could toss objects into areas they were never intended to be. In the “Forget About Freeman” level there was a chair that could be tossed over a rail into the adjoining area. I discovered that as long as I crouched down behind this skinny office swivel chair and slowly pushed it ahead of me, the alien warriors in the room could not see me because I was “behind” an object tagged as opaque.
Just across the street to the left of the Kings Row train station (if you’re coming out of it) is a small sewer access door, and a plaque. The plaque talks about how an old villain did something to the populous to make them walk endlessly in circles in that area.
The reason for this is that the style of sewer door there was not in the first release of Beta. It was put in during beta testing, but the pathing of the pedestrians were screwed up by it. Civilians would endlessly try to climb it at full speed, then slide back down. By the end of a night of testing, there could be half a dozen civilians ‘trapped’ there. Due to the slide-like nature, we called it ‘The Playground’, and would often start following the civillians and pretending it was a playground slide.