As it is quite often the case: it totally depends on what you want to achieve. Using Facebook eventually only makes sense when you're logged in – so that's probably he first thing you would want to do when visiting their website. Other websites might prefer the opposite approach.
We were just discussing this in a project I'm currently working on – and while the client first wanted to have the login fields present at all times, we finally decided it actually suits the purpose of the website better to have them on a seperate page. The client is a rather exclusive 'club' of some hundrets of people – so while having the login form present at all times would be user friendly for them, it would awake the wrong expectations to everybody else.
Personally I prefer form fields on seperate pages – also when visiting other people's websites. IMHO form fields often take too much attention off the actual content – and they're usually only needed in quite special situations (login/search). If I really want to login or do a search I'm patient enough to do the extra click. But maybe that's just my personal opinion.