As much as I'd love to describe the way that we do appraisals here at Hairy Spider, I can't. Being a one horse company there isn't much point.
However, my day job as a developer does get me involved in appraisals. They follow the familiar format of sitting in a room with your line manager (project leader, team leader, department leader, technical director, etc.) and dicussing your work. The discussion at some point turns to the uncomfortable question of strong points and weak points. Nobody likes these questions and you have to query the validity of them particularly when, according to my last appraisal, my weak points are my lungs: I'm asthmatic you see. Anyway, this is a great exercise for the line manager who has all the fun of a particularly sadistic medieval torturer.
Now the problem for me is that if I have a problem with procedure I'd like to feed that back to my line manager and if it's something the she is responsible for then I'd like that to go on their appraisal as an objective to be met. All the appraisals I've ever sat on have been one way traffic in that the developer has all the objectives that the line manager sees fit.
So in my fictional future where I'm in charge of what goes on, I think the company policy will be for peer appraisals. Where the system will be that a line manager will do the individual developer appraisals, but following these there will be a line manager appraisal where all the subordinates will provide feedback and objectives.
Ahh yes the future...