Netflix, of course.
One of the go-to names in streaming media, Netflix has loads of movies and television ready and waiting for you to stream to your iPad and mirror onto your television. Unlimited streaming costs $7.99 per month.
Your favorite media player app.
You can load up your iPad with movie files and play them on your television via any number of media-player apps. We recommend GoodPlayer, which is available here for $2.99.
Amazon Instant Video.
The Amazon Instant Video app offers Netflix-like functionality, getting you access to thousands of your favorite movies and television shows. If you're an Amazon Prime member, then you have free access to a majority of the content!
Check it out here.
You need a Lightning Digital AV Adapter...
One of the best ways to get video off of your iPad and onto your television is with this adapter. They're $41.29 on Amazon, which really beats Apple's own $50 price tag.
... and an HDMI cable like this one from AmazonBasics.
If you don't want to use a cable, try an Apple TV.
Apple TV connects to the internet via WiFi to bring you Hulu Plus, Netflix, and a host of other video options. It's $99 from Amazon.
If you're in New York, get Aereo.
Aereo is a service that lets you watch live over-the-air TV on your iPad and lets you record shows as well. This is all possible by "renting" one of several small HD antennas connected to a data center for $12 per month.
The service is expanding and will soon be available in other cities.
Check out Aereo here.