As TVs typically have a shorter life cycle than other electronics, they also have a fairly predictable price cycle, and it's easy to find the best time to buy a new TV. The vast majority of TVs are released, sold for about a year, and then discontinued when the replacement model comes out. If you want to be on the cutting edge, the best time to buy a TV is in spring/early summer, when the bulk of the year's new models are released. If you're a bargain hunter, though, there are better times of the year to make your purchase.

Above, you can see a simplified breakdown of the typical TV price cycle. New models are typically released at a fairly high price point. Early in the year, you're usually better off buying last year's model, as it'll be heavily discounted at most retailers as they clear out their inventory for the new models.
Finding The Best Deal
Every year, most brands release most of their new lineup in the spring. New models are typically released at a relatively high price, and most brands keep them at that price for the first few months after release, with a slight overall decrease over that period. By mid-summer, these new models tend to start dropping in price rapidly as retailers have finished clearing out their old stock. By this point, you can usually find the new model for around the same price as the one it replaces. These mid-range prices tend to stick until the holiday season, and TVs are usually close to their lowest price by Black Friday.
By the new year, they go back up to about where they were pre-holiday, then see a few cuts over the following months, leading up to the release of the new models in spring and early summer. Then you'll see a large decrease again, mainly because these TVs are discontinued.
The same trends are consistent for most TVs, meaning that the overall best times of the year to buy a TV are around the holiday shopping season and then once the next year's models are being released. For an even better deal, you could also wait longer, until well after the next year's models have been released, as prices for older models will usually continue to drop. Just keep in mind that by doing this, you run the risk of the model or specific size you want selling out forever.
ALL RETAILERS HAVE THE SAME PRICE
Several TV manufacturers - including Samsung, Sony, Sharp, and LG - have a Unilateral Pricing Policy (UPP). This means they set the prices at which their TVs are sold in every store. Typically, this means every store selling a given TV model will be selling it for the same price as all the other stores.
Legally, retailers don't have to honor this policy, and they can set their prices lower if they wish to do so. Legally, the manufacturers can refuse to do business with retailers that refuse to comply with the UPP; this is why all major retailers do. These UPP policies are also why recent years have seen fewer unique sales on televisions than in years past. Chances are that if a TV is on sale at Amazon, it's also on sale for the same amount at other retailers like Target or Best Buy.
Warehouse models
Many TV manufacturers also offer warehouse models (like Costco and Sam's Club) for a slightly lower price. Most of these TVs should perform the same as the units we've tested, but there are often some slight cosmetic differences, likely a darker bezel or a slightly different remote. They almost always come with an extended warranty. These models usually have slightly different model numbers; this is so the retailer can avoid having to price match with other retailers. For example, the warehouse variant of the Samsung QN80H is known as the Samsung QN80HD.
Black Friday Models
Black Friday, the last Friday of each November, is usually one of the best times of the year to buy a new TV. Many TV manufacturers release TVs with slightly different model codes from existing models in the run-up to Black Friday, usually by mid-October of each year. Contrary to popular belief, these usually aren't cheaper models with worse build quality or a cheaper panel. More often than not, they perform exactly the same as an existing model, but there will be minor differences, like a slightly different remote or different Wi-Fi specifications. Brands do this so that they can sell these models at a cheaper price point without having to price match other retailers or other deals.
Conclusion
While there are occasional deals on TVs throughout the year, people who want a bargain should do two things: buy their TV during the holiday shopping season or right when the next year's replacement models are coming out in the spring, and buy from a reputable dealer. Doing both of these things will ensure you get a good price on the TV you want.