well after their release
Well, yesterday I bought FEAR. Not really too old of a game I guess, but then again it's not exactly new if you get it for $20 or less.
I also didn't play Metroid Prime for ~4 years after it's release. Bad decision to skip that game for so long. I guess the only upside is I got it for $3.99
I didn't get KOTOR until almost 2 years after it's release, however getting KOTOR prompted me to get KOTOR2 as soon as it was released (for PC anyway).
I also had the original Tomb Raider for a long ass time, but never bothered to play it until just after playing TR: Legend.
I also bought some ports from the NES of games I'd never played before a long time ago, mainly the Zelda's and FFI, and they were originally released in some cases before I was even born.
I usually don't buy games new though, unless it's something special.