When an unregistered user gets to stackoverflow.com he will see:
As you can see there is no register link.
I think this is confusing since most sites on the Internet that sounds horrible offer "register" in there home.
I know this is done like this because of the "particular" login and registering process on StackOverflow, but new users don't know this, so, they might be looking for it.
This is tacitly done in the questions page:
So I would suggest the same is done for the home page.
Here are some ideas as it how it should look, most are just awful (except the last one) but the point remains, I think the register "concept" should be there somewhere/somehow: