One of the biggest players in the TV to smartphone game is obviously Netflix. Although Netflix doesn't release exactly how much content they have, the number of titles is reported to be around 60,000 -- which includes their movies. The app is free, but requires a subscription to their streaming service.
As far as video quality goes, Netflix is one of the best for streaming your favorite TV shows. The video quality and sound are great and you can pick up watching where you left off on another device (which is great for those long meetings at work or awkward family reunions). Don't worry about trying to search for titles on your phone's screen, the app will tap into your instant queue, and show you recommendations and viewing history as well. Unlike the Web version, however, you won't be able to search for actors or directors.
One of the biggest complaints about the Netflix app for Android is the amount of scrolling you have to do if you have a large queue. There isn't a button to go to the top of your list or a way to quickly scroll through the whole queue. Another drawback is the lack of current programming. If you're looking to watch TV shows that are newer than last season, you're probably out of luck. But the sheer number of other TV shows available, plus the fact that you can watch multiple seasons back to back, make the Netflix app for Android a great one indeed.