On my bike I usually carry the following. Admittedly some of this stuff may be overkill but I like to be prepared.
• tire levers
• mini pump
• patch kit
*
• Pedros Trixie tool (screws to bottle cage mounts with the wing screws shown)
• Spare tube
• Power Gel
• Nashbar multi-tool including chain tool and allen wrenches
• CO2 inflator and extra CO2 cartridge
• cheap/lightweight cable lock since bike theft isn't a big thing around here
[not pictured]
• Camelbak for hydration and carrying the 30lbs of crap around with me!
* I prefer the patches you glue on yourself. If you carry a patch kit it's important you understand how to use it correctly; I have seen several people on group rides who carry a patch kit but either have no idea how to use it or try to use it incorrectly.
And at home, in addition to standard non-bike-specific tools like wrenches and screwdrivers I suggest at least:
• bike work stand
• small set of allen wrenches (I have a set of nicer T handled allen wrenches as well)
• chain breaker tool
• bike grease
• chain whip
• various spanner wrenches for pedals, headsets, BB's, hubs, etc.
• BB removal/install tool
• Crank puller
• freewheel removal tool
• spoke wrench(s)
[not pictured]
• Other wrenches, screwdrivers, and a hammer!
• a nicer set of spoke wrenches
• torque wrench