Memento is a horrible attack, when used in battling that is. It instantly kills your Pokemon, and only sharply lowers the opponent's attack stats, which is easily remedied by switching.
However, it is quite useful in secret bases made for EV training. For example, you make a secret base in which the trainer only has six Lv. 100 Gardevoirs with Memento as their only move. You bring in, say, a newly hatched Lv. 5 Gastly, whom you want to EV train in Sp. Atk. You go to the base, fight the trainer, and gain the desired EV's as well as a whole lot of Exp, since the Gardevoirs are Lv. 100. They kill themselves, essentially, and you get the benefits.
And that's basically the only good use of Memento. Oh, and there's contests too, but who ever does contests?