If you have fond memories of wasting entirely too much time playing Crazy Taxi on your Sega Dreamcast, Mad Processor's Parcel Panic - Post Car Racer 3D [App Store] is really worth checking out. In the game, you play as a delivery truck driver on Tapiti Island, a strange land where customers expect their packages to be delivered in a matter of seconds or minutes instead of the days (or weeks) we're used to in the real world.
Starting the game, you have 60 seconds to get to the first seemingly random package pick up location indicated by a green circle on the ground. Once there, the bed of your truck is filled with crates and you need to race the packages to their destination. Guiding you to where you need to go is both an arrow, a mini map, and a dotted line showing you one way you could take.
Once you get familiar with Tapiti Island, you'll quickly realize that simply following the dotted line is not the fastest way to get from place to place as there seem to be shortcuts and ramps everywhere. Getting massive amounts of air also adds a few seconds of time to the clock, and when you successfully deliver your cargo, you're also awarded bonus time. The game continues until the clock reaches zero.
Also included is a free play mode where you can explore Tapiti Island. Although you may not notice it while you're frantically ferrying packages from place to place, the island itself is home to all kinds of varied architecture and overall, in my opinion, seems much more interesting than the repetitive cityscapes that made up the Crazy Taxi world-- Even though Tapiti Island is nowhere near as large.
The developer put together the following trailer for the game:
Really, the only thing I don't like about this game is the camera takes a bit of getting used to. Your truck is controlled by tilting, which is standard for games like this, but your viewpoint seems to always tilt to keep the truck level on the screen regardless of how much you're tilting your device. The driving physics themselves seem fairly realistic, so your truck doesn't turn instantly, but the way the screen will tilt all the way to the side makes it feel like it should be.
It's only disorienting the first few times you play the game, but since people have mentioned not liking games with cameras that tilt with the device it's worth mentioning that Parcel Panic is one of the more extreme examples of this. Even though it has a weird camera, Parcel Panic is by far the closest thing to Crazy Taxi on the App Store, and completely worth a look for that reason alone.
If the Crazy Taxi comparison is lost on you, Parcel Panic is a fun and fast paced driving game with tons of jumps, unlockables, great graphics with effects that scale depending what device you're using that I've really enjoyed since loading it on my iPhone.
App Store Link: Parcel Panic - Post Car Racer 3D, $2.99