Stranded Without A Phone
(iPod/Phone, may be iPad version, which would no doubt be amazing.)
It's an isometric hex-based survival game set on a randomly generated tropical island. It has a day/night cycle, random wildlife (fish and boars), and a great system for improvising things from your environment. It's a really amazing game, the deepest I've played on my iPod Touch.
You play an elderly scientist who crash lands on an alien planet (I believe) and is the sole survivor of his station. You're on this small island, with nothing at all, and your only ultimate objective is to build a radio transceiver, with parts you have to wait to wash up on the shore and collect. If you don't maintain your Hydration, Hunger, Injury, and Health, you die. You have to maintain them to survive the days you'll be spending there- hyd and hung go down constantly, if they're at 0 your health starts to go down, injury only goes up if you're damaged, and your health goes down faster depending on how injured you are.
There's a simple inventory, a function to search the ground for naturally occurring objects, a great list-based combining system so you can make anything from an axe to lemonade to a water skin to a battery (lemons, copper, zinc, and wire FTW). The combining system is based on items that are in your inventory or on the ground at your feet or at the hex in front of you.
It only has two small flaws- it doesn't teach you how deep it is or how to play it properly (the interface is pretty complex and it doesn't point out the tutorial at all, plus you can only quit by pressing your iPhone's home button), and once you have collected loads of items from the environment, the game starts to have some item list refreshing issues (though this may only happen on my 2nd generation iPod Touch with the really rubbish 4.0 software update). This lead my guy to eating some rotten boar flesh as the list hadn't refreshed; it still said it was normal boar flesh.
Great game though, I've made it to about day 15 or so. That must be 3 or 4 hours in. It's still pretty challenging and I haven't seen all there is to get from it. Great, great stuff.