They're completely meaningless but they make me play more games and make me play games in ways I normally wouldn't.
For instance, I just finished my complete playthough of Mass Effect (all missions except the random collect Asari writings and what-not) which I normally wouldn't have done except I wanted the rich achievement, completionist achievement, and Quarian ally. I was also trying to get the level 60 achievement, but finished at level 54. ;_;
Hell, I even used the shotgun because I wanted the achievement and ended up loving using the shotgun (I could one-shot most everything at the end of the game with it, and even one shot things from as far as way as the rifle could just hit things). If there wasn't an achievement for killing 150 with the shotgun, I probably would have just stuck with the assault rife and never touched the shotgun.
Achievements and trophies even make me replay games! Games like Uncharted, Bayonetta, and Bioshock I would normally never play more than once but since I get something for completing them on different difficulties or in different ways, I'm driven to do that.
And looking at the Wii, there are games I would like to try but I'm much less encouraged to play them because I don't get anything to show for it. I have Silent Hill shattered Memories which is supposed to be great, but I'm just not motivated to play it. I loved what little bit of New Super Mario Bros Wii but I didn't finish it and I doubt I will because there's no achievement driving me to finish it.
Or I guess I shouldn't say I don't want to play those Wii games, but I would rather play games with achievements/trophies first. I don't think I'll even like Heavy Rain, I'm sure Deadly Premonition is actually bad, and I know New Super Mario Bros Wii is better than both of those but I would much rather play the other two first.
A lot of people love to call achievements/trophies meaningless, and they are in the end, but they are probably the greatest thing to come out in this generation.