The one universally important tool is a repair stand. As others have said, buy one or build one. You'll be glad you did.

Beyond that, what you need depends on what kinds of bikes you work on. Most of the advice above is geared to European and Japanese bikes built before 1990. Newer bikes use mostly Allen (hex) fittings; older British or American bikes may have hardware in Whitworth or SAE sizes.

I'd highly recommend a Dremel tool. I use mine all the time, for cutting cable housing, for polishing rust off chrome, for making any of the ten zillion little fittings and adapters I always end up needing when I mix parts and accessories from different eras.

If you're dealing with bikes from a lot of different countries and eras, a digital micrometer is really useful. Measurements have become much more standardized lately.