9game starts by talking about the modes in the Android version of 2048, as there's only one. By tapping Menu and then swiping to the right, you'll find the Challenges mode. I should warn you now, they are VERY hard. I'm stuck on Challenge 6 but I'm still determined to beat it, even though I've tried more times than I care to think about (I told you it was addictive).
Now for the Android version, which has three additional modes to choose from: X-Tile, Survival and Practice.
In X-Tile mode, there's this annoying tile that can be moved but can't be summed, so it adds an interesting new obstacle to the challenge of getting that 2048 tile.
Survival mode (shown right) involves a timer, which is rather fun but so, so hard. You start with 15 seconds on the clock, and each time you merge two tiles with a value of 8 or higher, you'll get an additional 2 seconds. This one's for when you're feeling really ambitious.
Practice mode gives you a total of 20 undos, so if you find you've made a horrible mistake you can go back and change it. This'll set you up nicely for Classic mode when you're a bit more confident about getting that 2048 tile.