Check your local listings. The majority of the major television networks--ABC, CBS, NBC--all have equivalent networks in the majority of the rest of the world that show their content on a regular basis, just like in the United States. Check the local network or digital cable station listings to find out if and when your favorite shows are playing.
Buy a "Region 1" DVD player and "Region 1" DVDs. DVD players and discs are region coded to prevent piracy--only discs purchased in "Region 1"--North America--can be viewed on players manufactured in the same location. However, if you bring an American DVD player overseas with you, or order one from an online retailer, you'll be able to play all of your favorite TV shows on DVD.
Buy the shows on "Region 2" DVD. If buying a "Region 1" DVD player is too much of a hassle, the vast majority of popular American television shows have been released on DVD in the "Region 2" format. You can buy them at local electronics retailers and play them on DVD players purchased overseas.
Use the Internet. There are a number of ways you can watch American programming for free on the Internet, no matter which country you are in. Check the website for the specific network that shows the program you want to watch and see if any streaming options are available. Likewise, you could always use Hulu.com, which features hundreds of full episodes of popular American television shows.