If your chain isn't too badly fallen off, you can usually just shift in the opposite direction of where it fell off and the derailleur will usually get the chain back on without having to get your fingers greasy.
Be careful when you do this so as to not apply too much power when you're trying to do this. If you're in a really high gear and it happens, you can get off, hold your rear tire off the ground and turn the pedals. Works 90% of the time unless you got your rear chain jammed between the cassette and the spoke.
Edit: You can very often see this if you watch professional bike racing. When the mechanics change a rear tire it will almost always knock the chain off of the front chainring. They'll just shift into the proper direct (low if it's off the high side and high if it's off the low side) and then spin the cranks and the chain will come back on.
Be careful when you do this so as to not apply too much power when you're trying to do this. If you're in a really high gear and it happens, you can get off, hold your rear tire off the ground and turn the pedals. Works 90% of the time unless you got your rear chain jammed between the cassette and the spoke.
Edit: You can very often see this if you watch professional bike racing. When the mechanics change a rear tire it will almost always knock the chain off of the front chainring. They'll just shift into the proper direct (low if it's off the high side and high if it's off the low side) and then spin the cranks and the chain will come back on.