Assuming that you're actually trying to connect to your own router (sorry to state the bleedin' obvious), then make sure the router isn't set to only allow specific MAC (as in hardware, not Apple Mac) addresses to connect. It won't have been set like that by default, but some people do turn on MAC-filtering.
Other than that, I've seen odd problems that sound exactly like this with some routers like this, but only with Windows machines. Do you have other machines that can connect wirelessly? Are you running any VPN or network software on your Mac? It's not an old router that doesn't support 802.11g?
Are you broadcasting your SSID, and can your Mac see it? Again, some people 'hide' their network SSIDs, however this doesn't really offer any security, since many network tools will still find them.
You may of course know all this; apologies if so.