Many times I see athletes stranded where there is really no reason to be. Yes, we all have cell phones and a ride is a phone call away, but we should be more prepared and be self sufficient as cyclists. What if your ride isn't available? And, if in a group ride, don't rely on others if you get a flat.
What every cyclist (or triathlete) should have in a seat bag/jersey pocket/bento box:
Tube(s): I carry 2. Make sure the stem is long enough for your rims. Two lightweight tubes can be squeezed into most any seat kit.
Tire levers: Have 2, and know how to use them.
Patches: Get some glueless patches and toss them in there. They can be used as a patch on your last tube, or to patch up a small rip in a tire.
Tire boots: Cut your tire? No worries. Put a boot between the tube and tire and you'll likely forget it's in there and go another 1000 miles. You can either cut up an old tire and use it--a 3" strip with the tire bead cut off works best, or you can buy boots. An energy bar wrapper works well, too.
Air: CO2 is the choice when with a group--don't make others wait while you pump, but a small pump is good in case you run out of CO2 or if you want to save a few bucks. I use a Genuine Innovations SecondWind--pump and CO2 inflator in one! Carry 1 more CO2 than you have tubes.
ID: Copies of an ID card and your medical insurance card in case it's a really bad day. A Road ID is a better choice. Every rider should have one of these or something similar.
$20. You never now. I have a Nathan VitaBand--ID, medical info, and cash all in one!
Cell Phone: Last resort. Or first resort on a crummy day when it's time to go home and take a nap. Put this in a Ziploc if you sweat or rain is a possibility.
Put all this in a seat bag, or a Ziploc in your back pocket, and you're ready to ride!