I don't know if it'd be considered a "mission", but the Mr. Freeze fight in Arkham City. I guess you could say the mission would be "Return Ras al Gul's blood to Mr. Freeze to get the cure"
Anyways, I love how on the harder difficulties, the Mr. Freeze fight is like a final exam of Batman's stealth capabilities, requiring you to use every possible stealth take-down in order to beat him.
Elder Scrolls IV: Oblivion. I can't remember the name of the mission but it's for the Dark Brotherhood. Basically, you are put into a mansion with an assortment of other people who think they're a part of a contest. Everyone believes that a large sum of gold is hidden in the manor and the one who finds it wins not only the gold but the key to the house. The twist however, is that there is no gold and you are charged with the task of killing everybody else in the mansion.
The people in the mansion with you are an old woman, a former blade, a huge-ass nord and, two other people who I don't remember too well. You're told to kill everyone without the others finding out and if your charismatic enough and good at bullshitting, you don't even have to kill everyone yourself! It basically gets to the point where you and 2 others remain...depending on who you are nicer two, they will vow to help you kill the murderer...so of course, I wait until the old woman and the huge ass nord are left over and convince Ingvar that Granny Goodness has been killing everyone off. I laugh when he kills the old bitty with a single stroke then murder him head-on.
But in looking through everyone else's response, I have to agree with this one. Really, the Dark Brotherhood quests were my favorite part of Oblivion, but this one in particular was just loads of fun. A murder mystery where you get to be the sinister murderer? In Stewie's words "It's so deliciously EVIL!" Another fun one that's similar to this is when you have to Purge the sanctuary and kill all your brethren.
On a related note, there's a mission where you have to kill some traveling merchant who happens to be a pretty powerful mage. If you're lucky, you can come across him while he's out on the road and just jump his ass, but more often than not you'll have to find a way to stealth-kill him while he's in a city. I found him sitting in a tavern once, surrounded by witnesses so I couldn't just shank his ass, so I tried the ol' waiting game by slipping a couple Poisoned Apples into his pouch. After that I never saw him again. Unable to proceed with the Brotherhood missions, I just moved on to doing something else. About three days (real life days) later, I was doing a quest for the Mage's Guild when all of a sudden I got a quest update saying to go back to the Brotherhood to get my reward. "Welp, guess he finally at one of those apples." I just got a kick out of how I wasn't even focused on that quest anymore but still managed to complete it because somewhere out there in that big world of Cyrodiil, some poor NPC finally used an item I had planted in his pouch. :3