Well, I don't watch much TV, but there's two shows I do watch a lot, of the competition variety:
Name: The Amazing Race
Genre: Reality Competition
Basic Premise: Teams (usually 11 teams of two) race each other around the world, following clues to go to all sorts of locations along the way. In the various locations, they also have to perform various tasks -- an element of the show that is much more pronounced now than it was in the early years. The race is divided into several legs, with most ending with one team being eliminated, but the first team to finish the final leg wins one million dollars.
Recommended Viewing Method: I never watch more than two or three episodes in one sitting myself. There are 26 complete seasons with 11-13 episodes each, with the 27th now wrapping up. I personally consider the earlier seasons to be much better than the latest ones especially.
Name: Survivor
Genre: Reality Competition (again)
Basic Premise: 16 to 20 people are left in a remote location, usually an island or somewhere near the water. They are tasked to survive for 39 days using the various resources that are given to them -- although this aspect of the show has faded considerably over the years. Every couple of days, though, they have to vote somebody out of the game, and so considerable strategy takes place in this respect. At the end of the game, a jury made of voted-out players decides the winner from the final two or three.
Recommended Watching Method: I can never take more than two episodes of this in a row, but I also do considerable strategic analysis, so that helps bog down my brain. Each season has around 14 episodes, and 30 seasons have been finished, with the 31st in progress.