Every cyclist should know how to fix a flat tire. Tools are a personal choice, generally you only want to carry the tools you'd use. (I know that should be a no-brainer.) I generally carry:
1. a tire patch kit
2. a frame pump
3. a multi-tool
4. cell phone
In the tire patch kit I include a spare quick-link for the chain and a presta-shrader converter. On longer rides I may carry a spare tube too; just to save time in case of a flat. Thus equipped, I can fix almost any flat tire, as well as tighten almost any bolt that comes loose during a ride. If you keep up on your maintenance, other failures should be extremely rare. As far as where to pack it, that is why saddle wedges were invented.