WinRAR can handle most common archives (zip, rar, ace, and 7z I think), plus it's got that nice shiny file manager, so it's basically all you need for casual archive handling. If you want to go a bit further, WinRAR has recovery records and can handle SFX and split archives.
7-zip would be the next best choice, but it only has partial support for a few common formats (can read rar and zip, thinks it can read ISOs but can't) and is only good for making ridiculously customized archives (7z, split 7z (which makes no sense naming-wise and has very poor/no error checking or recovery), and a non-standard zip variant that nothing else can open).
If you need to extract things and want the best chance possible, even if you don't know what it is, Universal Extractor is your best bet.
I keep WinRAR and Universal Extractor in my context menu, with 7z, UHARC, and a few other obscure tools stored in a folder. That combo hasn't failed me yet.
Edit:
Because some people want to use a freeware programs, as it was specified by the OP, and neither WinZip, nor WinRar, non WinAce are free. Like I don't use either WinZip or WinRar, because I have 7-zip, which is OpenSource / free of charge.
ACE is a proprietary archive file format, so it can't be used in an OpenSource software, like 7-zip, and probably to implement it in other software, even freeware but not OpenSource, there is some licensing fee that needs to be paid by the software developer.
WinRAR isn't freeware, but you can get it
free, which is what the topic title says. There's both the trial version, which has a little nag box but works just fine (apparently forever, it hasn't turned off on me yet), or this:
http://www.win-rar.com/unpluggedinfo.html
Which is the portable, unplugged version and works just fine. The download is even from their site, so it looks like it's legitimate.
Edit2: And considering the OP is looking for a free program to extract a proprietary format, they're lucky anything exists at all.