Looking at router logs can be scarey. In the last few minutes I had attempts at unauthorised access from S. Korea, France, China and Chicago. You can become quite paranoid if you look at it too much, which is probably a good thing.
In general, your router firewall should drop all packets which originate from the internet as opposed to packets coming in response to your actions, like web browsing. Also remote admin should be explicitly disabled unless you have a VERY good reason to need to reconfigure your router when you are not at home. I don't know if your router allows it but I have mine set up to allow admin only from 2 specified IP addresses on my home (wired) network.
There are sites which will probe your internet IP and see if there are any holes in your filewall (ie open ports etc). Ideally the router will not respond at all and will be invisible to unwanted visitors.
