Drive Snapshot will backup a hard drive and skip bad sectors (as well as recording them in a plain/text log file) automatically (it's not an option that needs to be turned on):
Drive Snapshot
http://www.drivesnapshot.de/
I've used this tool on many occasions to recover data from failing hard drives.
Now, for a note of caution: As far as data recovery is concerned, depending on the cause of the bad sectors, more usage can actually make the problem worse and result in more bad sectors developing. SpinRite is an excellent tool, and I highly recommend it because Steve Gibson is a top-notch programmer with a specialized understanding of the inner workings of hard drive technology, but before using a tool that exercises the drive more like SpinRite does may still be more risky without first having a backup (that is, getting a backup before attempting further recovery is usually a good way to reduce risk).
1Thx for the extra info! – ctzdev – 2011-03-02T20:58:06.747
2> more usage can actually make the problem worse Indeed. One thing I would recommend when dealing with problematic disks (and discs) is to pause the read operation now and then to let the disk/disc cool down for a bit. That helps with not only typical overheating problems of electronics, but also lets the disc/platters shrink back down to their normal size since excess heat can cause them to expand slightly (which is often enough to throw off the delicate calibrations of those microscopic bits). – Synetech – 2012-02-20T19:43:24.353