dtgreene: Just remembered another one:
In Pokemon, to catch a Pokemon, you must throw a Poke Ball at it; the success rate increases if the opponent is at low HP or under certain status aliments. However, if you kill the Pokemon (or, rather, make it faint, as that's how the game describes the event of a Pokemon reaching 0 HP), the battle will end and you won't get to catch it. This is particularly important when you're fighting a legendary Pokemon, as if you fail to catch it before it faints, you never get another opportunity.
AlKim: Oh Christ. I remember running after one of those elusive legendary dogs around the map so I could whittle its HP down with False Swipe, a weak attack that cannot KO its target - once they have 1 HP left, the attack does no further damage. Then you go on a silly-ass chase and throw Poké Balls like they're going out of fashion, restocking when the critter runs off, sorting yourself to whichever location it now buggered off to and repeating the cycle until one of you gives the fuck up.
I think I remember getting a Smeargle with Spore and False Swipe.
(To get a Smeargle to learn these skills easily, get into a fight with a wild Smeargle, use the move on it so that the wild Smeargle Sketches it, then if you want it on your existing Smeargle, bring it out and then use Sketch. For Spore, you can take advantage of the fact that, in 2nd gen (unlike 1st gen), a Pokemon can use a move the turn it wakes up. Worth noting that, with these two skills in particular, there's no risk of the opponent dying prematurely.)