The ability to access online entertainment—streaming-movie services, YouTube, photo-sharing sites, and more—directly from a TV was once limited to high-priced sets. It's now available on many TVs, including midpriced models. Content varies by model, but many TVs allow you to use the remote control to order movies and videos on a pay-per-view basis from Amazon Video on Demand, Blockbuster on Demand, or Vudu, or from Netflix as part of a subscription.
You can connect an Internet-enabled TV to an Ethernet jack, but if that requires running a cable to another room, consider a TV that also has Wi-Fi, either built in or via an external adapter. Keep in mind that buying a TV with Internet access isn't the only way to go online. You can get the same content with an Internet-enabled Blu-ray player ($125 and up) or similar capability with a set-top box from Apple, Boxee, or Roku (starting at less than $100). Many of these devices have Wi-Fi.