It used to be my music collection that defined me, but these days my carefully ordered shelf of games is just as telling. These few boxes give away the fact that I'm introverted, cautious and enjoy human contact.
The games you keep in your collection define what sort of person you are, telling a story about not only your gaming history, but also your personality traits. If I could wander through your house and pick through the games on your shelves I could tell all manner of things about you - at least until I was discovered and arrested.
For example, if you have every Final Fantasy game ever released on every format, I could tell that you really don't like loose ends. Whereas, if you pick and choose only the best games, keeping hold of Time Splitters 2 and Second Sight whilst ignoring Time Splitters 1 and 3, I'd know you are more concerned with quality than just the latest thing - a purist.
Maybe you have a collection of multiple Advance Wars games - you are definitely someone who doesn't mind repetition. But if you have only kept Black Hole Rising, you're obviously a little fussier about particular play modes. If you've only got Dual Strike in your collection then you want as much crammed into your games as possible. Days of Ruin is the choice if you have more refined, less-is-more tastes.
Then we have the sports franchises. If you keep hold of a favorite version of Madden, Tiger or FIFA then for you, functionality is more important than visual form. Or maybe you simply prefer the Wii's Motion Plus controls for Tiger 10 rather than the high definition visuals of the PlayStation or 360 versions - you'd better face the fact that you are a pragmatist, valuing playability over visuals.
If you have more Platinum/Classics budget releases in your collection, you are patient enough to wait until the masses have moved on. Whereas if you have those first day special editions, the Halo 3 Legendary Pack for instance, you are a classic early adopter. But if your collection is peppered with repackaged editions - Fable II Limited Edition and Fallout 3 Game of the Year - you want the complete experience in one place; perhaps you don't trust that download content.
Traditionalist gamers stick to the original experience, as opposed to the revisionist who is quite happy with a re-worked classic. If you got rid of your PS2 or Gamecube Resident Evil 4 in favor of the Wii version then straying from the originally intended game experience doesn't bother you. But if you prefer the lounge friendly pointing of the New Play Control versions of Metroid, Pikmin or Mario Tennis, a modern update is enough for you to buy games a second or third time.