IANAH (I am not a hacker), but having researched this thoroughly, I decided it is possible to break into the NAT firewall of the Linksys BEFSR41 router (as well as the other 'cheap' routers that rely on NAT for security). It's very difficult, it requires some patience, and it requires some program that accesses the 'net in a repeatable fashion (plus an exploit on the OS that is being run). So, it's very tough but it is possible. What you need to do is watch the outgoing packets and keep track of where requests are going. Then you pretend to be an incoming packet, spoof your IP address and basically fake everything so that your packet return seems to be a reply to an outgoing packet request. Then you need to have an exploit for the OS or whatever is monitoring the port (like buffer overrun, or some other vulnerability) and using this you can hack the computer. I have never hacked a thing in my life, but I came across the above scenario when reading about NAT security.
Another alternative (which I think is possible, but I don't know for a fact) is, if the user isn't forwarding any ports, you can take advantage of the ability to access the router from the WAN (the 'net) port, put in a password pounder to just pound out passwords, and when you get the right one, you have access to the router. If the user is execeptionally clueless then the password will just the the default. Then you move computers onto the DMZ host until you find one that you can hack.
For the first, there are no really good ways to avoid except to stay up to date on security issues with your OS and browser. If there are no exploits known for your OS/browser, then there's no way to take advantage of the access that you've spoofed. You should also avoid running programs that access the net in a repeatable manner.
For the second (which, like I said, I'm not sure is possible), choose a really hard, long password with alphanumeric characters and capital letters. They give you a possible password of up to 64 letters and numbers. Mine is over 30 long, doesn't mean much of anything (it's in a relatively obscure foriegn language) and contains a whole lot of special characters. So, if you are worried, come up with a really complex password and you should be more than safe. Also watch your logs.
Having said all this, you need to worry a lot more about trojans and viruses and hardware dying than hackers. The more important your data is to you, the more important it is that you take precautions. But the NAT security on a router is fairly rock-solid. I disagree with Boberfett that it's "totally secure", but it is "reasonably secure" in my opinion. And I researched the issue pretty thoroughly on the Usenet and reading articles.