Memento was a pretty good movie based on Amnesia. It's about a man that can't hold any new memories in his head after some sort of accident (cant quite remember) and is trying to avenge the death of his slain wife. He covers his body with tattoos of all the clues he picks up on the way, but it's really interesting to watch from start to finish.
I think they did a really good job in creating the story and there aren't really any issues with the plot as I'm sure most similar movies will have. The actor who plays the main character does a great job with the blank stares and whatnot, and there is a good little twist at the end.
I think that if you are going to bring amnesia into a storyline in any way it has to have a detailed role. You wouldn't want to just bring it in briefly to smooth over a hitch in your plot.
If it is done tastefully it can still work regardless of how many times it's been done before, but it will be something that you have to constantly incorporate into the story in some way as to avoid plot errors.