Very much depends on the game, what is required, and what I get for it.
Any BioWare RPG, I'll do my damndest to run through it multiple times and complete each sidequest, get each ending and item.
I just finished SMG with all 242 stars. I had to take a few months between the first and second run through - I got the first 125 in about a week and risked OD'ing on the game. But it was a blast the first time, and it was neat running around as ***** the second time. However, it doesn't give you more than one last, rather lame, level, so were it a weaker game, I probably wouldn't do a second run through.
I have not finished TWIP yet, because I haven't gotten all the fish, but that's it. I doubt I'll bother with that.
Metroid Prime? Finished it once on normal. May go back for missed tokens and such another time, but I've got a stack of games waiting to be played now.
RE4? In the old days when I had more time I would have done all I could to get every last record on the Mercenaries levels, but I've got the real kickass weapons in the single player, and that's good enough for me right now.