VLC is an easy-to-use cross-platform video player that will work with Flash files as well as nearly any other video format you want to throw its way. You can even use VLC to convert your Flash video to another format, though I've had better luck with other video conversion software.
MPEG Streamclip works with PCs and Macs as a Flash player, and plays any other variety of video and audio formats. The program does a good job converting video between formats, and can also be used for basic video editing.
The Wimpy FLV Player is a super-simple Flash player that you download and install on your compter. Wimpy FLV works with both Macs and PCs, and lets you watch Flash videos from your computer or the internet. There are no extra features, so that's about all you can do!
As its name would suggest, NicePlayer plays nicely with a variety of media formats, including Flash. NicePlayer doesn't have any fancy features, but if you're looking for a straightforward, easy-to-use Flash player, it's a good choice.