You could carry fix-a-flat, etc, but I would only use it as a last resort. The problem with that stuff is that it can harden inside your tire, rendering it useless, and it can also stick to the inside of the wheel rim to the extent that either the rim needs replacing, or someone spends a couple of hours chipping it off.
In a lot of cases, you can fix a puncture using a cheap tire plug kit (check Amazon, they start at under $10), and if you carry a floor-standing bicycle pump that can handle a schrader valve, you can pump the tire up easily enough at the side of the road.
AAA would be the easiest option if you don't want to change it yourself.