I've looked at several forums like this one and this one but since Google changes their interface every couple days, they're all wrong.
Here's what my sign in page looks like today and I can't remove any of the accounts from the list:
First I go to gmail.com and get this:
Then I click Sign in with a different account and get this:
Best Answer
Make sure you go to google.com not google.ext (where ext is from your country).
From there log out from all listed accounts, and on the login windows, choose log in with other account.
This should give you this:
If you don't see the above at this point even, clear your browsercache, temporary internet files and cookies. Then try again.