I'm having the following problem: the customer logs in, is redirected to main page, but gets redirected back to login page. There is no error message.
On failed login with wrong credentials there is an error message displayed.
Login to admin works ok.
EDIT: this seems to be related to the website restrictions funtionality (Magento EE)
EDIT2: It is not the form key issue. Looks like that Magento does not recognise that the customer is logged in. If the website restrictions is disabled, the login appears to work (no error message, user redirected to front page, as should), but actually does not: the user simply in not logged in, login link is displayed etc.