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 simply place one drop of oil on the fan axis. Unfortunately you have to disassemble the LinkStation for this, then take the fan out and peel off a little sticker that covers the axis. But this will not take longer than 5 to 10 minutes. After doing this, the noise will be gone for another year or so.
Some other users had to completely replace the fan, or wanted to replace their (LS2) fan with a more silent model. See the FAQ for more info on this.