Madagascar: Escape 2 Africa
does a fairly good job of weaving seemingly random mini-games and unusual objectives into a cohesive story.
The story itself has the former City Park Zoo-residents deciding that they need to leave Madagascar, but when their ill-conceived plane, that was cobbled together by the colony of lemurs and piloted by the penguins, crash lands in the African savannah, the guys must either try and fix the plane or learn to live in the wild.
The game actually takes on a variety of styles based on which character(s) you are controlling. While Alex, you play through platformer-like worlds, while Marty's objectives are either races where you use his sprinting ability or use his kick to knock soccer balls or other items into the air. Gloria typically involves swimming while Melman will either fly around with his helicopter ability (of course) or balance upon a rolling ball.
I have to say some of my favorite objectives were the missions involving the penguins. These typically involved Private navigating hostile environments in order to collect parts for the plane.
Besides the game's Story Mode, you can also buy decorations and clothes for the 100 monkeys you will have to get together to help you re-build the plane. There is also an arcade where you can play a select few of the mini-games from the main storyline. Interestingly enough, these are available at the beginning and don't need to be unlocked by encountering them in the main story (like most other games do).