Originally Posted by Seizedpost

For threaded headsets you can often get away with a very large adjustable wrench. For cables and housing almost any cable cutters will do, even the $7 one from Harbor Freight. What you will need for cable housing is an awl or something pointy to open it back up, as cutting it tends to pinch the end shut. Come to think of it, I bet a ballpoint pen would work.
For bottom brackets, if you're just regreasing all you need is a lockring wrench and a crank puller. If replacing then you need to remove the fixed cup too.
Access to a bench vise can be extremely helpful if you're restoring neglected old bikes. They're great for removing stuck bb cups, seatposts, and freewheels.