Internet TV may not be the wave of the future yet, but it will be someday. For now, you can get most, but not quite all of the TV programs that you love somewhere on the internet (legally).
Probably the most basic way to stream internet TV is with Hulu or Hulu Plus.
Hulu is a free streaming service with programs from all over the world. Need your Anime fix with Tower Of Druuaga? It’s there. Can’t live without the BBC puppet show for adults called Mongrels? It’s there, too. They also have episodes of currently-running hit shows from the US such as Glee. On the free version of Hulu, you have to wait for a week for them to appear, but on Hulu plus ($7.99 per month) you can watch the current shows the day after they air on the network. http://www.hulu.com 
If you want to have a wider variety of programming to your TV, but don’t have an internet-capable TV or DVD player, a good option for you might be Roku.
Roku is a palm-sized box that streams internet video through your wireless router to your television. The great thing about Roku is that if you haven’t made the step up to a high-def TV yet, Roku hooks to standard-def TV’s through the included A/V cable. All Roku units also connect to high-def TV’s through the HDMI port, although you have to buy the HDMI cable separately.
Roku ranges in price from about $50 to about $100, depending on what features you want, including the limited edition “Angry Birds” Roku, which is red and has an Angry Birds bird on the surface, and includes the game at no additional charge for about $90. All of them are capable of 720p HD, but only the two higher-end versions are 1080p capable.
Roku currently features hundreds of channels, many of which require membership, either stand-alone or in another service (Netflix, Hulu Plus, etc). There are also religious channels, sports channels, news and weather channels and pay-per-view services such as Amazon on demand. Also, with the optional Roku games remote (standard with the $100 Roku, $30 purchased separately) you can play games like Angry Birds, Pac-Man and Galaga. http://www.roku.com/ 
Another option that I did a stand-alone piece on a while back is Playon.
Playon allows you to stream many of the same services as Roku, but also has the standard version of Hulu rather than just Hulu Plus, and streams content from channels that don’t allow their content to be streamed on the web outside of their own website, such as CBS. So this is where you’d get your Big Bang Theory fix. Once you purchase Playon, you install it to your computer and then use your computer as your media server to stream the content through a Playon capable device (gaming system, etc.,) and to your network-enabled TV. Playon is $5 month-to-month, $20 annually or $50 for a one-time purchase. You can bundle Playlater to this, which uses your computer as a DVR for Playon programming for a total of $8 monthly, $40 annually or a one-time cost of $100. Both of these are after a two-week free trial. http://www.playon.tv/index.php 
Gaming systems are on board with this now, with apps for Netflix and Hulu Plus among others available for your PS3, Xbox or Wii.
Of course, for those of us who like it all in one place, many TV manufacturers are now making internet-capable televisions, which stream many of these services straight to your television set, either wirelessly or hardwired. For instance, I have the Vizio VIA TV (which stands for Vizio Internet Apps) and love it. It not only streams services like Netflix and Hulu Plus straight to your television set, it also allows you to keep in touch with people through Facebook and Twitter.
So when you are ready to step up to internet TV, decide which route you want to take, purchase the right item, make sure that you have high-speed internet (1.5 meg DSL minimum) and enjoy!