Depends on your router, but some do have the ability to do advanced things, or to flash with custom firmware that turns it into a linux box which you can do a bunch of stuff on it (eg install squid, etc)
Depends what you're trying to do as to whether it's worth it or not
If you're trying to use it as a proxy for a computer inside the network, then you're really not gaining anything as it's generally a NAT router and you're already appearing to be that IP on the internet.
Or perhaps are you trying to configure other people's routers to be proxy servers that you can then use to access the internet as their IP? That would depend on the proxy setup and any possible blocks/firewalls put in place by the ISP.
