Gekko Mahjongg World Championship 1.15
This has animated menus, tons of different game modes -- many are only available in the full version -- and an online ranking system.
All aspects seem done well. There isn't really a reason to not download this game.
There are tons of additions online at the game website that can further your Mahjongg experience. Both the classic and championship modes offer variety with over 1,000 different board layouts.
If playing a relaxing and well-done Mahjongg game while competing all over the world for the top score is right up your alley, download Gekko Mahjongg World Championship.