It can run its own apps (lots of unix apps). On some systems (Z80 ones with a CP/M compatible memory map) it can run CP/M emulation. On 6809 it can run some Flex apps and other bits but I don't think Brett ever finished making that really useful. There's still quite a lot of work to do to get it self hosting but you can build C programs natively on it for some processors.
With the right cards it can also run ZX81 applications, although they run a bit quick so 3D Monster Maze is a reaction game, and 3D Defender is wicked. Does make Catacomb rathe more playable 8)
Fuzix is really an art project showing what you can do on a Z80 board and how to write tiny programs. If Symbos is "What would happen if you wrote AmigaOS on a Z80" Fuzix is "what would happen if you ported Unix to an 8bit micro"
Alan