I'm the latter. I've tried to compile complete libraries in the past, but I never made even made it to 10% of any list. I have a very impressive Bonk/Zonk collection that spans across many consoles and a couple handhelds, but my interest fizzled about 5 games shy of completion, plus I'm thinking about selling it off.
But now I just accquire games that I enjoy, or game series that I like. It's easier for me.
Yeah, I'm a little confused about the whole thing. Basically, I know what games I want - what's "next on my list" so to speak, but some time ago, when I'd bought all the first choice of (reasonably priced) games, people pointed out a load of other great games I wasn't necessarilly aware of.
Then, there are games which are quirky and weird. Some, like Be Ball are great, some like Kickball are less to my taste.
And after THAT, you've got the cheapo games that don't look like much but are pretty darn fun, like Motoroader.
I think the plan is to pick and choose the games as and when they appear, snapping up bargains. Then when I get to the point where all I have left to get are Mahjong games and Darius Alpha, it would be stupid not to complete