If you catch a noisy fan soon enough, it can probably be saved.
The reason it's making a grinding sound is that the pores of the sintered bronze bearing inside the fan's motor has lost its internal oil, and is beginning to slip and stick repeatedly (much like the action that causes the squealing of rubber tires on a road).
To repair a fan, first remove it from the assembly it's installed in just enough to get access to the back side of the motor. This will be the part that has several radial spokes holding it to the frame. There will be a sticker on this, usually marked with the fan's manufacturer and ratings; peel it up carefully from one side. If there is a rubber or plastic plug below this, pry it up. Add one drop of oil (for a small, CPU cooler-sized fan) or about 2-3 for a larger fan. Be careful not to get it on the plastic surface the label sticks to.
Now, replace the plug (if present) and stick the label back down. Reassemble the equipment and you're done.
I highly recommend you do this on fans in new equipment as well, as a preventative maintenance measure; it greatly extends their life. A fan should only require this once in its lifetime. Ball bearing fans are usually quite well lubricated at the factory, and generally don't need this; if one is running rough, oiling it doesn't help much and it should be replaced.