Unless you see everyone flipping out on Twitter or the Cblogs that they can't login, it's probably just something on your computer eating your cookies.
Did you alter your browser's privacy settings or install some extensions? Try disabling those from the extensions system or browse Incognito with extensions off to rule this out.
Most commonly it's Adblockers, Antivirus, Anonymous Browsing, etc. which are notorious for breaking site logins. See if your Norton, McAffee, etc. aren't blocking cookies.
Good security programs always run in the background, so closing the icon or right-clicking 'disable' doesn't mean they are fully shut down (Avast definitely does this). Try a different browser or in anonymous mode to help pinpoint the issue. In most cases you can fix it by whitelisting our domain (it varies by software).