Is there a technical term for someone being burnt out on something they enjoy? What I mean is like how one might tire of a typical everyday activity they enjoy if they indulge in it too much, like how if you listen to your favorite album too many times you eventually won't be able to enjoy it anymore. I guess this would also be analogous to how addicts develop a tolerance to their drug of choice.

I figure it is an interesting phenomenon that must have a very large affect on our behavior patterns so there must be a technical term for it. I wanted to know so I can look into any research there has been on it.
There is no specific term for this entire phenomenon because there is more than one psychological theory playing a role in your overindulgence or "binge". Fatigue from repetitiveness, durability bias, and habituation all play a huge role in determining how long you can listen to a certain song before its gets repetitive and boring. 
On the other hand, tolerance from substance abuse has its own special term: Drug Habituation.
You would be best off searching scholarly journals using the keywords fatigue and habituation.

Further Reading:

https://en.wikipedia.org/wiki/Habituation
http://changingminds.org/explanations/theories/durability_bias.htm