The Linkstation is amazingly quiet, at least the PPC-based models like the LS1. After one year or two years of operation however, the LS fan may make some buzzing noise.
For some users, it was enough to oil the fan axis. Unfortunately you have to disassemble the LinkStation for this, You don't have to remove the circuit board but it might help. Carefully lift the panel out and you can see the fan which is held in on some springy plastic fingers. Ease them apart and you can lift the fan out. The wires are not too long so it is a little fiddly.
Next, using a Stanley knife, carefully peel back the label from the fan to expose the bearings. Don't damage the label, it is used to keep the bearings covered. Now apply a drop of lubricating oil, 3-in-1 oil works. Also you can pack the bearing area with some LB10 grease using the tip of a screwdriver. Wipe off any excessive oil/grease and stick the label back on. Assembly is the simply the reverse. 
Some other users had to completely replace the fan, or wanted to replace their (LS2) fan with a more silent model. The stock fan is a 40mm x 10mm 12V fan, ADDA part #AD0412LX-G76 (see http://www.addausa.com/model_index.htm for more information). It can be replaced with most any equivalent fan. It may be easier to get the three pinned smart fans so that the system wont lock up.