Use the largest wire that you can fit into the space (conduit, access hole, etc.). Generally (very generally, Hellosailor is correct, it depends on the length, insulation temperature rating, etc.) 10 AWG is good for 30A, 12 AWG for 24A, 14 AWG for 16A. However, for long runs the voltage drop in the wire may rob power from the appliance so you may want to go to a higher gauge.
The breaker or fuse rating is generally matched to the wire gauge it protects. This means the largest breaker you should use with a 10 AWG wire is 30A. Smaller is OK but never larger. If you feed a smaller fuse with a larger breaker, the wire gauge to that smaller fuse needs to be the same gauge as the circuit wire. What this means is that if you are putting a 2A fuse in line to an instrument, and feeding that fuse on a circuit protected by a 30A breaker, the wire to that 2A fuse needs to be a minimum of 10 AWG. The wire from the fuse the instrument may be 18 AWG.
Match the wire to the breaker and the breaker to the wire. If you have a circuit that opens a breaker because of the amount of current draw, do NOT just install a larger breaker unless you check that the wire is rated for the current the new breaker will allow. If you have a 15A breaker or fuse on a 14 AWG service, and need more current, you will need to change the breaker AND the wire.
There are two types of fools...
One says this is old, and therefore good..
The other says this is new, and therefore better...