So long as it is not a ball-bearing fan you can easily disassemble, clean, and lube the bearing assembly - in general this is a BIG help. i have taken fans that no longer spun and brought them back into full service without so much as a tick. However, some are not so lucky and make a little noise.
Check this out:
Get the fan out of your system.
Remove the sticker if it has one that covers the bearing opening. (This is on the non-fanblade-side of the fan.) Some bearings have a little round plastic cover.
You will need a tiny flat-head screwdriver or sewing needle-like device for the next part.
you will see the end of the fan's shaft sticking up with a ring around it. Though the ring looks contiguous, it is actually a C-Clip, split at one spot. Pop it out delicately - however, they can take a bit of abuse and still go back together.
Pay attention to the order of things - the fan will come apart at this stage. Generally there is a washer on both sides of the sleeve bearing, and sometimes little rubber o-rings.
Pull it all apart and clean stuff with rubbing alcohol. Use Q-tips soaked in alcohol to really soak the bearing and clean it up good.
Now, before reassembly be SURE to lubricate the shaft and the bearing. You will need enough lube to make all metal parts wet, though not dripping. You can remove excess if need be.
What to use for lube? A lot of people suggest household 3-in-1 oil. Do not use WD-40. I use Synthetic 5-w30 motor oil. If you do not have any special lubes, use baby oil - it's simply mineral oil. Just be sure to use a light lube, these things spin fast and a heavy lubricant such as automotive grease or vaseline will not lubricate properly. (Vaseline is actually a decent lube for other things, since it is a petroleum lube. Go figure.)
Be sure to re-cover the bearing access hole. Use duct-tape if the sticker no-longer sticks. You may need to clean the oil from the plastic with alcohol to get the tape to stick..
BTW, be sure of course to clean the fan blades and housing while you're at it
And blow the dust out of the heatsink.
I clean fan bearings and lube them all the time - I don't remember the last time I came across a "dead" fan. I choose to re-lube every 6-12 months.