Can tubes be used in tubeless rims as well as tires? I've gotten a bike with very nice tubeless wheels, however I have little experience with fixing or replacing tubeless tires/wheels. I would much prefer to be able to put a regular mountain bike tube in the tire and rim without problems or much hassle.
Is this possible?
Yes - take off the tire and the tubeless valve, clean up the rim, put on some new rim tape and then install a tube + tire. 

If you're running tubeless and you have a failure, you can always just pop a tube in and continue your ride. And tubeless has its advantages (lower pressures since you can avoid pinch flats), so you may want to embrace it.