I heard about The Hunter on an episode of Shut Up, We're Talking. It's a beautifully designed free-to-play hunting game. You start out with a basic rifle and scope, binoculars, GPS, and camera (squee!). You travel through a lush hunting preserve, looking for signs of your prey. Your GPS will show you the radius and direction your quarry is headed based on the types of tracks you find, and the stalk begins!
The wildlife AI and hunting mechanics are very realistic. Running noisily through the brush or standing up in a clearing will scare the deer away. Holding your breath while sighting your shot improves your aim. The environments and sounds are beautiful and very realistic (complete with day and night cycles), and for an explorer and virtual shutterbug like me, being able to go all 'nature photographer' in the game is a cool bonus. Also, you get points based on how impressive a specimen you shoot, and there is an online ladder comparing the scores of every player. So competitive types should have some fun too.
As you complete quests, you can gain the ability to hunt more than just deer, too. There's a cash shop for buying new equipment as well as social networking tools. If you like hunting or are curious about it, it's definitely worth a download.