Almost all of my game purchases are on Steam now. There are several key advantages:
1) No boxes, no manuals, no discs. True, I could just throw out everything but the disc and CD key, but I feel bad trashing a game box / manual for some reason, especially the nice plastic ones.
2) No more hunting for patches and updates to each game. Steam does all of that for me.
3) No need to lug around discs for games. I primarily game on my desktop, but every now and then I'm out and about and feel like firing something up on my laptop. More often than not, I couldn't simply because I didn't have the game installed on my laptop and didn't have the disc with me. With Steam, it's just a simple download.
4) I don't have to run to a store to buy a game that I want, or buy it from an e-tailer and wait for it to come in. A lot of my favorite games these days are impulse buys from Steam sales - Titan Quest, Trine, DogFighter, Defense Grid, Amnesia: The Dark Descent, STALKER: SoC, etc. Nothing like treating yourself to a new, random game to play after a rough week.
5) Having the social tools (friends list, browser, etc.) built right into the in-game interface is awesome. Being able to fire off a quick message to someone without having to alt-tab, or being able to look up a map or hint in games where alt-tab sometimes results in a hang or crash is a plus in my book.
There are downsides, of course - sometimes parts of Steam are down and games will fail to update or launch, sometimes Steam is buggy and causes problems that a stand-alone game wouldn't have, there's always the looming (though remote) possibility of having your account compromised, banned, or Steam shutting down (all resulting in loss of your game library), etc. The problems have been few and far-between for me, though, so the good far outweighs the bad.