i.TV is a free television listings app. It has a lot of ads but at least it's free. One of the most significant updates to this app is its ability to stream ENTIRE television shows and movies. Granted, not a lot of shows are streamed at this point. And some movies, like "The Golden Compass," have bad streams.
One of the best streaming television shows on i.TV is the classic "Star Trek." You can watch it in its original 4x3 format (pictured) or you can fill the screen.
Right now, the best way to watch live or recorded television on your iPhone is Orblive, at least until SlingPlayer is released. But both of those apps require hardware that you may or may not have.
i.TV requires absolutely no additional hardware, but the streaming content probably works better over 3G or Wi-Fi. Unless you'd rather have a no-frills T.V. listings app like What's On TV?, i.TV is a must-have for iPhone owners.
The MacRumors Forums is keeping track of which shows are being streamed so that you can just search for it instead of flipping through the listings.