The contents of a cyclists seat bag can, literally, mean the difference between a great ride and one that you would soon forget. Sure, we all would like to have every ride be trouble free, but let's face facts. Stuff happens when you are on the bike and if Murphy is along for the ride, it seems like things head south at the worst possible time.
Well, first things first. You need to have a good pump. Not CO2 cartridges, a good pump. CO2 is fast and easy, but if you somehow screw it up or your spare tube has a leak or you get multiple flats you may be walking. So get a good pump and know how to use it. OK. If you really want to use CO2, fine. But, bring a pump along just in case the CO2 fails. It will, trust me.
Inside your seat pack you should have at least the following essentials. Two, or even better, three tire levers for prying off the tube. Tire levers seems to break when least expected so make sure you have at least two. A spare tube is critical. Wrap it in plastic or keep it in the cardboard box to protect it from getting punctured in your seat bag. If you ride in areas that are known to be flat-prone either carry a second tube or better yet, a patch kit. If your patch kit uses glue, make sure the glue has not dried out. I carry both glue and glueless patches just in case.
One last essential is some form of tire boot. If your tire gets a cut that would allow the tube to poke through, you need to put something inside the tire to prevent that. I use Tyvek, the strong, paper-like fabric which is used by Fed Ex and the USPS for their mail envelopes. In an emergency, a dollar bill or energy bar wrapper will suffice.
Some non-essential, but very handy items include a spoke wrench which can come in very handy if a spoke lets go. Of course, that means you have to know how to use it. It's pretty simple. Loosen the two spokes on the opposite side of the rim which are on either side of the broken one. Use small turns until the wheel clears the brakes. A small screw driver is handy for making on-the-road derailuer adjustments.
A set of allen wrenches, 3mm-6mm, are handy for adjusting seat height, stem, and other allen key fittings on your bike. Also, a chain tool is useful if you are the type who seems to break things. I carry a $20 bill and a credit card in my seat pack. Money can't buy everything, but in a really tough jam it just might help.
Obviously, your mileage may vary(YMMV), but there's a good start. Enjoy the bike, but if Murphy shows up for the ride. Watch out!