My ISP just sent me over a box and now I am online. I am afraid of beeing exposed directly to the internet. Is there any website or web app which can check to which level my machine is accessible from the internet?
You could try googling for the word "port scanner" to find a web service which will do a security check for you. However, please note that anyone offering to do this kind of check for you might also be gathering information in order to misuse it.