For quite some time now, we have been getting sporadic reports of mysterious login problems, mostly with Internet Explorer but sometimes with other browsers on other OSes.
There are a other few known problems with proper fixes, and those include:
a) not able to be logged in to multiple sites on the same domain at once. The fix for this is: <code>ini_set('session.name', '.example.com')</code>
b) login works, but you still appear to be logged out. The fix for this is to just press reload.
c) Users login to www.example.com but don't show as logged in on example.com. The fix for this is to put in an .htacces redirect so that www.example.com automatically becomes example.com. See <a href="http://drupal.org/node/77106">Login doesn't work or must be done twice</a> in the Troubleshooting FAQ.
However, if you have tried to log in to just one site, and even a reload fails to show you as logged in, and multiple host names are not the issue, then you are facing this problem. If you are BOTH a) able to reproduce it reliably and b) are familiar with development processes like patching, then please comment on this issue and I will try to help you find a solution.
First advice: try to reproduce with another browser on the same OS. If it happens with two browsers, then it's more likely an underlying infrastructure issue, which I won't detail here. However, if it does not happen, then reinstall the browser. If it's OS-bound then reinstall the OS. Try to reproduce again. If not succeeded, install back all the crap that your browser had and try logging in from time to time. When it breaks, then post here.