I'm constantly surprised at the large number of great games of the PSP that completely slipped me by the first time around. And the best thing is, these games are currently going for pocket change. I picked up Echochrome (which I had BITD, but is still worthy of owning and replaying) and Echoshift, a semi-sequel.
Echoshift has you playing and replaying levels, manipulating platforms and switches within a time limit, in order to get to the exit. However, you'll never get to the exit on your first try.
You see, you keep replaying the level over and over again, alongside the ghost images of your former attempts, and you're judged by the number of attempts you use. An example might be a series of ledges running towards the door, and a long ledge running underneath it. On your first run, you might have to walk underneath, standing on switches to connect the ledges overhead, timing them so that your future self can cross over in time.
It quickly gets more complicated, and like chess, you have to think ahead to where you're going to be and when, on the next go and even the go after. And then you get one little thing wrong on the first attempt, and it will be impossible to get the best grade.
At the moment, I'm quite far through the standard levels, though it's getting tricky, but even after that, each stage has two variant modes. I picked up this game for about £2, and I can't put it down.
Now is the time to grab yourself a PSP and start buying up all the great games!