Is it depth, length or addictiveness that produces a game you simply can't put down? Arguably a smattering of all three.
At first we thought this list would be pretty easy to compile, but we had some agonising decisions to make - it just goes to show the quality and depth of software now available on handheld platforms.
But, ultimately, we tended to veer towards games that not only give you a lot of bang for your buck in terms of longevity in the main quest but also demand that you go back to experiment and explore some more.