As a minimum you should always carry a patch kit and a mini pump. Tire levers are only necessary if you can't pry the tire off by hand. This is something you should ascertain beforehand.

I recommend carrying a spare tube as well, because if your tube fails anywhere near the valve stem, then your patch kit won't help you. However, this type of failure rarely occurs, so it's not necessarily a must-have item.

If you want real peace of mind, then invest in some Mr. Tuffie tire liners for about $18 a pair. They fit between the tire and tube and provide an excellent layer of protection against punctures. The downside is that you lose some of the suppleness of the tire, and after a year or so, the ends of the tire liners eventually slice the tube wide open.