There's Crazy Golf and then there's Wonderputt. One connected course of 18 holes, and a series of beautifully-animated, wildly imaginative sporting puzzles. What seems at first glance like one simple journey to the top of this strange course soon becomes an unpredictable chain of transforming landscapes (such as a field cows being abducted by aliens to clear the path to the holes) and sudden jumps to new worlds (such as the inside of a deconstructed missile). It's wonderful to look at and largely a joy to play, although occasionally it's tricky to get the precision required for delicate shots. See all Apps reviews.
Of course, the meat of the game lies in self-betterment. The first time around you'll be marvelling at the oft-changing, architect's drawing-like look, but thereon in you'll be trying to beat your score. It's Crazy Golf played against yourself, and the simple drag-to-whack controls still manage to offer opportunity for some neat trick shots. See Best iPhone and Android apps.
It's a bit of a one-trick pony, perhaps, but what a trick. It takes the tedium and the posturing out of golf, turning it into a thing of delight and surprise - a not a sun-faded plastic windmill in sight. Take a look at Group test: what are the best iPhone apps?