Jagex's Security Certificate has been revoked, hence why you cannot log in.

For those on steam/not using Jagex launcher: the reason for not being able to log in is due to aforementioned certificate no longer in place.

You may notice your browser/antivirus outright disallowing you from accessing even the main website. This is also due to the certificate.

This is something Jagex will have to sort out. For now, Jagex Launcher or mobile should work if you wish to log in.