RT (Request Tracker) is sort of an industry standard for ticket tracking. It's very powerful but very complicated, and tickets can get out of hand (like any ticketing software) when queues are not maintained regularly. I used it at a job a few years ago, and because of the lack of maintenance, it was awful. Now I work for a place where they know how to run it well, and it's terrific.
The default install is pretty generic, but I think you could configure it fairly easily to have custom fields for each ticket (customer name, customer phone, machine type). I'm not an RT admin, though; I'm a Linux admin; I just use RT, and as a user, I'm more than satisfied with it.