At the start of the game, just out of the simple options, there are four different dungeons you could begin with. Or skip straight to the main one instead of a starter. Or go to the bandit village, or kill something friendly, or fight something out in the wilderness. The game being randomly generated as it is, your first kill (out of, by the time you reach a point where it's relevant, hundreds at the very least) could be any of about 40 different creatures.
Later on, you can get the Courage skill. This stops you from getting weakened when outnumbered, and is therefore one of the game's best skills. To do this, you have to reach level 10, not be evil (chaotic alignment, in the game) and visit an old barbarian for a sidequest.
His sidequest? Go kill 20 of whatever your first kill was. Quite aside from the fact that depending on what your first kill was, this may not be possible, you probably don't remember unless you specifically wrote down your first kill. For which you would have to know about this quest.
Much later on, if you want the best ending (and, incidentally, the game's best weapon by far), you have to go kill Filk, the quickling bard. Now, quite aside from his being one of the nastiest monsters in the game, he's in the Infinite Dungeon, which re-generates floors whenever you enter. The floor he's on has to do with the first creature you killed. The floor number is equal to the number of that creature that you killed. For example, 31 jackals? Floor 31. And if it's jackals, rats, goblin rockthrowers or something, the floor number could be over 100. Oh, and if you made your first kill something unique because of this, sure, it'll be floor 1. You will also have to find some other way to get the Courage skill, like using a wish.
Rather sadistic, no?