For the road:

Spare tubes (presuming you have inner tubes), tire levers, pump. It's unlikely that a properly maintained bike will need anything else other than these. A friend of mine never takes any tools whatsoever and just says repairing at the roadside isn't worth it - unless you're going far out from home. I laugh but I do think he's right. I don't always have someone to call on to pick me up so having a spare tube, some levers and a pump can be a lifesaver.

At home I would get:

Lube/grease, chain oil etc..., plenty of old rags, chain link extractor, screwdrivers (you might only need one type), allen keys (might as well buy a set 4/5mm are most common), pliers, cable cutters, a good adjustable wrench, any relevant 'special tools' to get your crankset, bottom bracket and cassette off (these are dependent on your parts) and some spoke tools.