Most failing drives had no problems before they begin to die, and visible signs like BSODs occur only if the "right" files are compromised. Many errors can go unnoticed until you access the affected files again.
Just last week one of my NAS' harddisks was stopped because of i/o errors, a s.m.a.r.t. test on my PC confirmed them. Fortunately, a immediate backup showed only 18 damaged files out of the thousands on the NAS. I still have to check if I have intact copies of those files in one of my regular backups I make every other month since the data on the NAS doesn't change that often.
In retrospective, I can say that having backups does wonder on one's nerves in case of hardware failure.
So, just to be (reasonably) safe I would strongly recommend a s.m.a.r.t. test of your drive and a backup of all data whose loss would give you more than a shrug of the shoulders. The test is easily done on most operation systems and it may save you from even more distress.
