Basically, anything with Iain M. Banks's name on it is going to be action on a massive scale, great ideas, laugh out loud humour, and soul-searching darkness, all rolled into one. You're not going to go wrong picking up any of his books. But these are some you'll really want to pay attention to.
The Player of Games stars the Culture's top games player, Gurgeh, who is blackmailed to go on a secret mission for Special Circumstances, taking on a brutal alien empire at their own particular game, and the stakes are far higher than he could ever imagine. This is a novel where you just have to take a deep breath every so often before plunging back into the action, because it really will screw with your mind. This is recommended as a good introduction to the series -- it's action packed, it's faced paced, and it's a rewarding story.
Excession mostly concerns the ships who are called on to investigate a strange intrusion into Culture space, and which gradually reveals a whole level of reality they weren't even aware of before. This won the BSFA Award.
Look to Windward describes an attempt to blow up an Orbital, an artificial world where millions of people live, as revenge for the Culture's interference in a long-ago war. It's the novel where you realise that the Culture isn't a static society but is actually evolving, growing older, maybe beginning to contemplate its own death.
The novels of Iain M. Banks helped to kick start the British Renaissance of the 1990s and also the New Space Opera, so if you love his books you're also advised to look out for some of the other books that emerged out of those movements.
The Fall Revolution Quartet by Ken MacLeod, Banks's childhood friend, is an obvious place to start; each volume takes a different version of Trotskyist politics as an underlying theme in a story that starts in a near future Britain and ends with a war against uploaded beings around Jupiter.
The Quiet War Quartet by Paul McAuley covers thousands of years of human habitation across the solar system, starting in the relatively near future when energy and enthusiasm are driving people ever further out but their efforts have to be directed towards trying to prevent a war between the colonists in the outer system and the authoritarian regimes left behind. But by the end of the series humanity is retreating as the various human habitats crumble and decay, but a mysterious message from the stars could reinvigorate things.
The Xeelee Sequence by Stephen Baxter, one of the most consistently reliable of hard sf authors, whose monumental series of novels and stories range from the present day to five billion years in the future when the solar system collides with the Andromeda nebula, during which time humanity becomes one of the most powerful races in space.
For big space opera with grand ideas and exiting action, give Alastair Reynold's Revelation Space series a read. It's got it's own thing going on -- a different sort of story than the Culture, but in my opinion, just as exciting.