FLV to MP4 Converter is a free video converter for Windows. It is a very basic application that only supports conversion of video files between a couple of format pairs. The graphical user interface is probably the simplest one I have ever seen. There are only eight buttons. Five of those buttons are used for output format selection: MPEG4, MPEG4(DIVX), MPEG4(XVID), MOV(Quicktime), and MP4 for Sony PSP. The other three are used to add files to the conversion queue, remove them from it, and start the conversion.
Once you have added files to your queue and selected the output format (all the files on the queue will be converted to the same format), you can click on "Convert to MP4", which will open a window asking you where you want to save your file. There aren't shortcuts for your Desktop or My documents folders, so you have to browse manually to get there.
The conversion process went quite smoothly in my testing. I converted files to MPEG4 and MOV just to test a few of the formats. Both of the files that I got played well on VLC and I didn't notice any problems whatsoever.