The number-one situation cyclists will face on a ride (aside from experiencing the awesomeness that is riding) is a flat tire. To fix that, you'll want either a spare tube or a patch kit -- or both. Of course, these are useless without something to pump them up! A frame pump or a C02 inflator will take care of that. Make sure to bring a cartridge for the C02 inflator. (They make devices that are both, but my experience is that they tend to do both jobs terribly.) Also, make certain you know how to change a flat. If pressure is important to you, get one with a pressure gauge.
Tools: Unless you're on a loaded touring bike, you'll want to keep your saddle bag light and bring along a multitool, as opposed to full-sized tools. I won't recommend any one tool, but something that includes the three sizes of allen keys and a chain tool will handle nearly any situation you're going to repair by the side of the road: Broken spokes, a split chain, a loose rack, adjusting a slipped seat-post, a rattling fender.
Duct tape or electrical tape: Wrap a small amount of it around a short pencil and toss it in your bag. You can use this to fix grip tape, repair a rip in a bag, or hold a headlight together. You can also toss a zip tie in there while you're at it.
Spare batteries are helpful if you have lights or a cycling computer.
I always bring along a cell phone.
A first aid kit is always a good idea. You can pare it down to the essentials, especially if you're on a supported ride, but it's a good idea to be able to take care of yourself until the sag wagon arrives. If you have a medic alert tag or a card, bring that as well. (I keep a tag on my body as well as one on the outside of my trunk rack bag.)
Water: I can't stress this one enough. Bring as much of it as you can carry comfortably, and always fill up when you have the opportunity. Dehydration is no fun!
This is a pretty minimalist kit. If you want advice on a kit for touring, there's a thread here on the site about just that.