Everyone knows to carry a spare tube with you when you go riding. That way if you get a flat, you can put the new tube in and make it home. However, you will need an air source to pump up that tube. Sure, sometimes you can cheat fate and always have flats near a gas station with free air refills.
But I wouldn't count on it.
Enter the Topeak Mini Morph
The Topeak has several different Morph models of pump, and the Mini Morph is the smallest. It rides discretely on the frame of your bike, typically somewhere around the water bottle mount, there for you when you need it.
When you need air, you just unclip it from your frame, attach the hose to your tire, and flip out the little foot stand. You can then stand on the foot stand and keep the Mini Morph steady while you pump.
Because the Mini Morph is so small, I've seen a lot of riders just stick into their jersey pocket. Sure, it sticks out, but it seems to ride ok back there. Typically, though, I would recommend mounting it to the bike.
The Mini Morph works with Presta, Schrader and Dunlop valves. You actually have to unscrew the heads and switch out the rubber grommet on the inside to convert it for the different valve types. I think it is pretty simple to do it, but you might want to practice when you first get the pump, just so you are comfortable.