Can I trust a hard drive that has had to reallocate sectors?

In my experience it's a toss-up. I've had one drive that had some reallocated sectors and a nasty whine that ended up outlasting some drives that gave no warnings before dying a miserable death. I actually chucked it because it was so noisy, rather than data loss.

However, for me, personally, at the first sign of problems in a drive, I backup then swap it off. Drives are cheap, online backups are cheap and if you're anything like me, your time is better spent elsewhere than trying to recover a drive.

Rather than just ditching the drive, you might want to just keep an eye on it first, to see if the reallocated sector count increases. If that count continues to increase, the drive is finding and mapping out more and more bad sectors.

I guess it depends on what this drive is doing - is it "mission-critical" or on a server? If so, I would be more nervous than if it's in a home PC not doing a whole lot (as long as you make regular backups of the data, which of course you should do anyways).

Edit: I just downloaded and ran CrystalDiskInfo on my harddrive here at work (an always-on PC, as we're a 24-hour operation), and it's logged 7739 power on hours and has 100 reallocated sectors.

For those who don't know, reallocated sectors are:

Count of reallocated sectors. When the hard drive finds a read/write/verification error, it marks this sector as "reallocated" and transfers data to a special reserved area (spare area). This process is also known as remapping, and "reallocated" sectors are called remaps. This is why, on modern hard disks, "bad blocks" cannot be found while testing the surface – all bad blocks are hidden in reallocated sectors. However, as the number of reallocated sectors increases, the read/write speed tends to decrease. The raw value normally represents a count of the number of bad sectors that have been found and remapped. Thus, the higher the attribute value, the more sectors the drive has had to reallocate.

Source: Wikipedia

I have drive that has 165 of them for a long time now. They all happened at one time and never increased since (two years ago). I would just closely monitor that figure. If it is just one time increase, do not worry.