Search Hulu.com, TV.com or TVGuide.com for full episodes of shows. Hulu is a TV show and movie aggregator and streams TV shows the day after they air. TV.com and TVGuide.com have fewer full-length shows than Hulu, but are additional options.
Go to a network's website for shows that are shown by that network. All the major networks such as ABC, CBS, and NBC offer their shows online. Cable networks such as Bravo and Lifetime also offer their shows online. These networks offer some full-length episodes along with clips, highlights, and previews of episodes and shows.
Check out TV shows on DVD from your library. Libraries are an overlooked source of free TV shows. You can borrow DVD's from the library with entire seasons of your favorite shows.