Where do you live? A lot of people that have satellite reception are out in pretty rural areas, so you may not have access to either over the air broadcast television, and/or high speed internet connections. So a lot of these options may not be well-suited for you.
There are five major providers of non-cable television content that you may want to look into: Apple, Amazon, Hulu, Roku and Netflix.
Netflix: $8/month can give you access to its online content, which is heavy on television shows, light on major motion pictures. Another $5/month can get you 2 DVDs a month to your mailbox.
Amazon: $99/year gives you access to even more online content, also heavy on television shows. I don’t have this service, but I know plenty of people who like it. The $99 plan is for Amazon Prime, which also gives you access to all sorts of Amazon perks, like 1-day shipping (with caveats). They’re being pretty aggressive these days acquiring content, and recently got HBO to give them access to nearly their entire library (minus a few fancy baubles, like “Game of Thrones”).
Hulu (Plus): Also $8/month. Has a solid corner on the market for recent content - they get shows just a few days after they air, versus waiting for things to come out on DVD for Netflix and Amazon (no, Netflix and Amazon don’t send you DVDs (other than Netflix’s DVD service…), but they don’t have the rights until it’s on DVD). It’s essentially a DVR for people without a DVR. Note that even for the subscription-based Hulu Plus, you will still have to endure commercials. It’s the cost of early access to the content.
Roku: For as little as $50, you can get a device that will access Hulu, Netflix, and Amazon services, as well as a bunch of random crap as well. You will need some sort of device to access the various provider content (unless you’re just going to watch on your computer rather than your TV), Roku is a well-built little device that you plug into your TV. (Be aware that Roku’s website is really misleading, and lists a bunch of channels that you can access via it, but you’ll need a paid subscription to actually watch (usually a cable subscription).)
Apple (TV): Like Roku, Apple has come to market with a nice little device that will access a bunch of service providers, Netflix and Hulu being the main ones. It does NOT access Amazon, however (they’re competitors). You can connect to any of your Apple-purchased media with this device, and have easy access to purchase shows and movies through it as well. They cost $99, and you can find them used pretty easily.
Amazon (again): Note that Amazon just went to market with an Apple TV competitor device, which does a lot of the same stuff, minus have access to the Apple store.