The problem is with blocking (or corrupt) cookies from Microsoft.
Please allow
[*.]live.com
[*.]microsoft.com
to save data in your cookies settings.
You must also allow the above in your Javascript settings.
If the problem is caused by corrupt cookies, then delete the above two cookies group and login again.
Thank you @TheRealMystic for this perfect solution. I see that you posted this multiple times, yet people continued to report the same problem. I guess most readers did not have advanced technical knowledge to understand what you mentioned. I will elaborate it here for the benefit of our readers:
When you are unable to login to a particular site, it is usually caused by one of two reasons mentioned below:
1. Cookies from the site saved on your browser has become corrupt. 2. The site is unable to save cookies on your browser.
If you have not restricted your browser from saving cookies, then the reason you're unable to login is due to problem 1 mentioned above. In this case, you'll have to clear cookies from that site and login again. In this particular case, you'll have to clear all cookies from live.com and microsoft.com as mentioned in the solution.
But if you are unable to login because the browser is blocking the site from saving cookies, then you'll have to configure the browser to allow cookies from the site to be saved. In this case, you'll have to make an exception for the two groups of cookies mentioned above:
[*.]live.com
[*.]microsoft.com
Once the above are added to the exception list, you'll be able to login again.
Please note that [*.] prefixed to a domain means all websites belonging to the particular domain.
You'll have to add these to the exceptions list here:
Google Chrome: chrome://settings/content/siteData
Microsoft Edge: edge://settings/content/cookies
The above applies to all browsers, and this is where you'll find them in Chromium based browsers (you can simply copy the above address, paste it in the address bar and press ENTER/ RETURN).
SOLUTION 1: Delete Corrupt Cookies
By default, most browsers allow sites to save cookies, so if you haven't changed that under browser settings, the problem in your case is due to corrupt cookies, and the solution is to delete them and login again. I believe this is the case with most users who have reported the issue here. Cookies saved in Chromium based browsers can be deleted here:
Google Chrome: chrome://settings/content/all
Microsoft Edge: edge://settings/siteData
Look for a similar setting in other browsers.
SOLUTION 2: Un-Block cookies
And as has been mentioned in the solution, Javascript too must be enabled for the site. Please note that this too is enabled by default. So if you have disabled it under browser settings, then either enable it or make exceptions for the above two groups of cookies here:
Google Chrome: chrome://settings/content/javascript
Microsoft Edge: edge://settings/content/javascript
The above applies to all browsers, and this is where you'll find them in Chromium based browsers (you can simply copy the above address, paste it in the address bar and press ENTER/ RETURN).
Hope this provides clarity to readers, and the issue is resolved for everyone.