I would highly recommend the first three books he wrote in the Culture Series. Consider Phlebas, A Player of Games, and Use of Weapons.

I enjoyed all of the series, but these three really made me realize how amazing the author and the concept of his universe really was. Consider Phlebas is told from the point of view of someone who despises the Culture, which, as an introduction to the series, provides a really unique viewpoint both within the book, and is also generally an interesting literary tool.

A Player of Games is my absolute favorite. I've given copies of this to several friends. It addresses the human problem of what does one do with themselves in a post scarcity existence, especially when advanced AI can just run and do everything.

Outside of the Culture series, I also highly recommend the Algebraist and Feersum Endjinn (sp?).

edit: I forgot to include "Against a Dark Background" in the outside Culture series recommendations. I've read that one a few times, it's quite good. At one point there was talk about making it into a movie, but I haven't heard anything about that in awhile.

Use of Weapons, Player of Games or Excession.

The fairly recent Surface Detail was also pretty good, although somewhat horrific in that it deals with the idea of virtual reality hells.

My Wife just read SD on holiday and thoroughly enjoyed it, liking the characters. I'm pretty sure that it's her first Culture Novel.

I started with "Consider Phlebas" after a suggestion here on HN (that I read Iain Banks), and I don't recommend it as the starting book, it was bit of a letdown (though it's an ok book).

I'm now reading "Player of Games" and it's far better, though maybe the introduction to the "Culture" universe was worth reading the first book.

It seems "Use of Weapons" is the best one, I haven't read it yet.