Apex Video Converter Free is a free video converter. It supports a few input formats: AVI, MOV, QT, MPEG, WMV, RM, VOB, DAT, 3GP and MP4 and it supports similar output formats. This free version only allows you to convert files to AVI DIVX and XVID files.
This converter doesn't have a very intuitive graphical user interface. Being used to all the nice interfaces out there, I found this graphical interface a bit old-looking and complicated. My biggest problem with it is that it isn't easy to choose what output format you want to use. The problem is that instead of listing formats, the converter lists codec names, so you see names like Intel IYUV, Microsoft RLE, VP62, etc. It is definitely way easier to select a conversion profile and not having to worry about figuring out which is which.
I tested the app by converting a file into MOV using the H.264 format. I got a warning saying that the format I selected wasn't available in the free version but I could test it anyway. So I did, and the resulting file didn't show any video. Audio played fine.