Free TV shows can be watched online at Hulu, TV.com and U-verse. Not all shows have free episodes available for online streaming though, and some offer only a selection of episodes, not the whole series or the most recent.
Many episodes on Hulu are available through subscription only, although there is a free one-week trial period at the start of the subscription. Hulu offers a wide variety of shows; not only American, but British, Korean and Japanese, as well.
TV.com has recent full episodes of a select group of shows available, as well as clips and previews from many others.
AT&T U-verse has a wider selection than TV.com, with full shows and clips both available. Like Hulu, U-verse offers shows that are currently airing, as well as those that have already ended. The most recent shows on U-verse that have just aired are only available through subscription, but relatively recent past episodes and clips are all available for free.
ITunes and Amazon Prime are two other services that offer video streaming for TV shows and movies. They have some free shows, but most require a paid subscription or are only trailers or clips. Both have very up-to-date selections available for streaming.