I have mentioned Virtual Villagers a few times lately. The creators also make Plant Tycoon,® “a gardening sim game where you nurture plants and experiment with increasingly rare and valuable species. The object is to breed and cross breed plants until you find the 6 Magic Plants and solve the genetic puzzle.” They also have a virtual fish-breeding game along the same lines.
Of course, these are offline games. If you are looking for online massively multiplayer breeding, you might try Virtual Horse Ranch. (It says right at the top that this is a “strategic” MMO horse sim game.) Google led me to a surprisingly large number of online virtual horse breeding games.
And people say there is no innovation going on.
Seriously, wouldn’t robust animal/plant/whatever breeding be a neat addition to your game’s trade skills? Don’t just give us a “breeding” skill that increments up: throw in some real Mendelian genetics. A Tale in the Desert has some things along these lines.