Can't log in to websites on Safari, anyone know whats wrong?

I have an issue with trying to log in and out of websites. Every time I try to log in to something, It starts to log me in and then redirects me back to the log in page like I never did anything. This started when I still had Snow Leopard and I hoped that when I upgraded to Mountain lion it would sort itself out, but it hasn't, its still broken. I also can't log out of twitter. It comes up wth a plank page and '403 Forbidden: The server understood the request, but is refusing to fulfill it.' written on it.

I have downloaded Chrome to use and everything works on there but I really would like Safari back. I can't for the life of me figure out whats going on.

Any ideas on how to fix it would be much appreciated!