The answer to the, "Why 15A or 20A circuits" is really a code question. The smallest wiring allowed by the NEC for a power circuit in a residence is 14 gauge with 12 gauge being common. Since a 14 gauge wire will carry 15A, it's typical to install a 15A breaker on a 14 gauge circuit. Likewise with 12 gauge and 20A breakers.
Sean's (and others') suggestion to use 10 gauge wire in a 20A circuit is to reduce voltage drop in that circuit. 10 Gauge wire will carry 30A and could have a 30A breaker installed in the circuit. From a power delivery standpoint (up to 20A, of course), this circuit won't be any different with a 20A or 30A breaker installed. However, one might be able to find a higher quality 20A breaker for the same price as a regular 30A breaker.
The thing to remember is that wire is sized to carry a load and the breaker is sized to protect the wire, not the other way around. So, while it's OK to install a 20A breaker in a circuit wired with 10 gauge wire (your electrician will look at you funny, but what does he know?), it is NOT good (or legal) to install a 20A breaker on a circuit wired with 14 Gauge wire.