My basic/most frequently used tools include:

• Metric Allen keys
• Small torque wrench with Allen bits (for carbon fiber frames/parts)
• Small screwdriver
• Cable cutter
• Needle-nosed pliers (crimping cable ends)
• Chain breaker
• Tire levers
• Pedal wrench (not necessary, but nice to have.)

My metric hex wrench set mainly gets used on vintage bikes, but is good to have. I've collected other tools for specific jobs, like wheel truing, cassette/freewheel/cog removal and replacement, crankset service, and bottom bracket service.