Here's the standard kit I carry when riding in the bush. Although I've never flatted or broken down on the road, these are the same tools I use in the shop, so I know what I need and how to use them. Everything fits into the little tail bag with a some room left over for lunch.
From top left to bottom right:
1. Tail bag and protective rain cover on my ghetto frame which mounts over a 1-gallon RotoPax
2. Spare socks
3. Front and rear tubes
5. Carabiner (can help when rigging a hoist for bike)
6. Emergency reflective mylar blanket (protects against cold, heat, rain)
7. TP, hand-sanitizer and lighter
8. 8mm and 10mm sockets
9. 4/5/6mm hex Y-tool
10. Folding 1/4 socket drive with extension
11. 10' of 9mm static line (e.g. for towing or rigging a bike hoist)
12. Silicone nylon tarp. Weighs nothing, compresses down, creates a big shelter.
13. Mesh bag for tools
14. Big adjustable wrench
15. Mountain bike pump
16. Two tire spoons
17. Folding saw
18. CO2 compressed air cartridges and filler valve
19. Microfibre cloth (for visor, first aid)
20. Details map on Teslin
21. Tube patch kit
22. Gerber multitool
23. Windproof lighter
24. Spare AA batteries for GPS (although it's also powered by my bike)
25. Two protein bars and a Clif bar (easier to think straight when I'm not hungry)
26. LED headlamp
27. JB Weld (not shown)
28. Pen, mechanical pencil, paper (not shown)
What would I add or change? The large adjustable wrench is unnecessarily heavy and should be replaced by a dedicated axle wrench for my front/rear wheel nuts. It's on the shopping list. Also, a roll of duct tape can come in handy. For longer rides I'll also add a long-sleeve wool shirt as a dry, warm backup. With this kit I can spend a night out or work on the bike in the rain.
Edit: I've since improved the tool selection.