The tools I reach for most often:

-a Y-wrench with 8, 9, and 10mm heads
-a Y-wrench with the three most common hex heads (whatever those are!)
-a 15mm wrench for rear axle nuts and pedal removal/installation

Bike-specific tools I need for larger jobs:
-a chain breaker
-various freewheel tools for removing freewheels (unfortunately, there's no one standard though the SunTour two-prong will serve you well)
-a bench vise (particularly for wheel work)
-a set of cone wrenches and a small adjustable wrench for adjusting hub cones
-bottom bracket tools: lockring tool, pin spanner, fixed cup wrench
-crank puller
-headset wrench
-a hammer
-good wirecutters for snipping cable ends cleanly
-not as good wirecutters for cutting housing

That list is what I use on probably 95% of the bike work I need to do. The other 5% is made up of fairly esoteric tools that are great fun to have but not essential.

Neal