Darlington with 3.3V
The TIP120 will work at 3.3V as well. You do not apply a voltage to a bipolar transistors base, but you apply a current to the base. The resistor between your micro controller and the TIP120 will convert the voltage to a current. You might need to reduce the resistance your base resistor a bit at 3.3V. 

Using a Darlington transistor can be effective for loads with a high voltage that are switched often, but are only switch on for a short time. If you switch a low voltage load, e.g.: a single LED, a motor running at 3.3 V volts, then bipolar transistors and especially darlingtons will be very ineffective. MOSFET can often be just as easy (or even simpler) to use and losses at the transistor will be smaller. Between collector and emitter of a Darlington transistor you will always lose around 1.2 V, no matter how much current you are switching. This is especially problematic if you are operating at high currents and low voltages. 
See for example these tutorials on how to use nFETs as a switch:
http://www.hobbytronics.co.uk/arduino-tutorial9-power
http://bildr.org/2012/03/rfp30n06le-arduino/