Object Fix Zip is a free tool which can try to recover corrupt, damaged or partially downloaded ZIP archives.
The program is constructed as a wizard, which makes it very straightforward to use. Add the files you'd like to repair in one step, choose the actions you'd like to carry out in the next, and it'll go to work on your behalf.
In theory, it seems as though Object Fix Zip should be able to help with most problems. It can test an archive to confirm the nature of any corruption, for instance. There are options to create a good ZIP file from the broken one, or, if that's not possible, to at least recover as many files as it can. And it can work with password-protected archives, too (as long as you know the password, of course).
A quick test of the program left us unsure of its abilities, though. We simply stripped the first two bytes of the header from a test ZIP file, and, oops - that alone was enough to defeat Object Fix Zip. It claimed our file wasn't a valid ZIP archive and refused to do anything with it at all.
Object Fix Zip may not be quite as effective as the authors claim, then. But as they're giving it away for free, it's hard to complain too much, and certainly you've nothing to lose by giving it a try - it just might be the tool you need to make a broken ZIP file readable again.