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Renting movies via the Play Store is okay, but IIRC you only get them for 24 hours. In my opinion, the best option is really Netflix, as someone else mentioned. The money you'd pay for Play Store content is much better spent on a monthly Netflix subscription, just based on their large amount of content. I would also highly recommend Crackle, which is free! Lots of cable providers are making the leap to mobile apps as well; for example, Comcast has Xfinity Player, which allows you to watch On-Demand movies and shows on your phone.
For TV shows, I'd recommend Hulu Plus for mostly the same reasons as Netflix. I'd also recommend free apps TV.com, and AMC Mobile if you watch any AMC shows like Walking Dead or Breaking Bad.
Hope this helps!