I created a circuit that uses a transistor to run a small (1.5 - 3v) motor. The transistor I used was a 2n3904 NPN. I calculated Beta to be about 11 when it's hooked up to an Arduino the base resistor I used was 47 Ohms and it worked well.
Given that I moved the circuit from the Arduino to a HiTechnic prototyping board, It's digital pins only put out 3.3v and from what I can tell (they don't say this online or in any documentation) the current is really tiny, about 8mA. Because of that it seems like I need use a different transistor - at least that is my guess, because even when I put a base resistor with 0 Ohms of resistance the motor barley turns and the current into the collector is barley 170mA.
To get a better idea of what I am doing. I have essentially taken this video tutorial and migrated it to this setup and I am using the Arduino to turn it on and off using the wire library and bitWrite.
The motor I am using is a Radio Shack Model: 273-258. It says it is .18amps to .25amps at no load, it will start spinning at just over .21amps.