Some Web sites offer free, bootlegged copies of TV shows. I don't use those sites and I don't recommend them. There's a lot I don't like about current American copyright law, but without it, you wouldn't have any new television shows, books, music, movies.
Youtube: Along with cat videos and regular folks spouting their personal philosophies, Youtube hosts a lot of professionally-made television. And parent company Google is pretty serious about keeping copy-protected material off the site unless the copyright holders have given their blessing. Just search for tv shows full episodes. Or search for a particular show, such as mad men full episodes. Monty Python has its own channel, and there's a lot of full Mystery Science Theater 3000 episodes here.
Hulu: The free version of this extensive service offers The Daily Show, South Park, The Vampire Diaries, Law & Order: Special Victims Unit, The Simpsons, and other current series--as well as classic ones. There are limits, of course. As a rule, free Hulu only provides five full episodes per series; but they're usually five recent episodes.
Your favorite TV network: Go to the Comedy Central site and you'll find a smattering of full episodes. News/opinion channels like Fox News and MSNBC offer everything from the previous day's show. Broadcast networks like ABC and NBC stream selections of new episodes.
And speaking of broadcasts, you can still buy an antenna and get free TV without even an Internet connection.
Finally, you can get an enormous amount of entertainment over the Internet for a very low price. For only $8 a month, you can subscribe to either Netflix or Hulu Plus. Their shows aren't always brand-new, but the options are huge. For instance, rather than the five recent episodes of Saturday Night Live you can get on free Hulu, the Plus service offers all 743 episodes dating back to 1975.