My 9800GTX has been ok for years, but suddenly one day when i turned on my PC, i noticed the fan was extremely loud, loud enough to be heard 10 metres away. I know it's the GPU fan because i can restrict it's movement and the noise will stop.
My system specs are:
Foxconn G31-MXP motherboard
intel Q9550 CPU
You should easily be able to remove your GPU panel. I remember the one on my 9800GT being just 3 screws away. I still think there is dust clogging the heatsink under where you can't reach so the heat doesn't transfer properly and the GPU is sending signals to the fan to speed up because it thinks it's hot.
But if it's not that, maybe it's just that the cooler's time has come. I mean, 9800GTX is an old card. You could try replacing the cooler, if you don't want to get a new GPU.
dirty needs cleaning (already mentioned by esteemed colleagues)
one of the bearings have gone south, sometimes tapping the fan will quiet it for awhile. (preferably while off)
The solutions in that case are replace cooling system with an aftermarket, (not cost effective) Riding it out and living with it. The last solution would be to replace the card.
bearing in the fan....that leaves live with it, replace the cooling assembly, or more wisely replace the card. I wouldnt bother putting money into an aftermarket cooler for an old card, that could have something else go wrong with it after repairing it.