Can you register domains with an existing tv show? I found a tv show whose name hasn't been registered yet so can I do that?
Yes, you can do this. I suspect that a letter will shortly follow from the TV show's attorney, much as BenQ suggested. I guess the question is why would you want to do this? It is not likely that there will be any reward in this venture. Many years ago, "squatters" would buy up all manner of domains in the hopes of selling it to the businesses that needed the domain. It is not a very viable business these days as no one cares, any more.
You should check out the ongoing battle between http://yourather.com and the toy company that TMed the term "Would Your Rather": http://blog.yourather.com/post/70907897801/dont-say-would-you-rather Probably nothing is going to happen while you're small, if you happen to grow, expect a lawsuit.
Of course you can, but then please do find some very good lawyers to defend the inevitable law suits that will follow!