I`ve got some in my cupboard and the expiry was May 2011 so yes, it does expire. I don`t know if it goes off but as it`s of animal origin I wouldn`t want to use old stuff.
Actually I can remember when I bought it because my mother was in hospital in Oct 2008 and I made a chocolate torte and bought the gelatine. That gives it a shelf-life of 2.5 to 3 years, probably.
I have used gelatine well after it's use by date (I suspect over a year after it should have been used.) It worked well and there was not any noticeable taste off it.