Magento login for admin/customer works fine with Firefox and IE. But sometimes we are not able to login in chrome. This is caused by session cookie compatibility in chrome browser. So sometimes in chrome you will not able to login or in some case you need to attempt login multiple times. For that you just need to disable session cookie by commenting few lines of code in magento core.
You just need to comment some following code in
$cookieParams = array(
'lifetime' => $cookie->getLifetime(),
'path' => $cookie->getPath(),
'domain' => $cookie->getConfigDomain(),
'secure' => $cookie->isSecure(),
'httponly' => $cookie->getHttponly()
There might be some cases in you are not able to login even you tried above solution. In this case there may be some extra cookie is creating which are preventing you to login. So you need find which cookie is causing problem.
Go to Admin -> System -> Configuration -> Session cookie management.
Make sure you have set correct settings as per screen shot. Now clear your browser and magento cache. Try now you are able to login.