Depends on the design, goals and intended audience.
Form fields are harder to ignore than most page elements and have a sort of gravitational pull on the eyeballs, so you can easily imagine situations where it's better to avoid them. Like, say, on public marketing pages for first time visitors to a microblogging app that's way hard to explain to your average non-blogging Yahoo-using grandma in flyover country.
I typically put a username / password box on any pages I want people to be logged in for. Now, obviously, this includes pages that they must be logged in for, but those pages should enforce authentication more strictly; But what I really mean are the pages that don't 'require' authentication, but for any number of reasons, it is preferred.
Also, I've always believed that the 'two boxes on a page' approach draws them torwards the login, and acts more as a call to action than Twitter's dropdown approach.
As alabut says though, use where appropriate.
One click to show is better than one click to load a wholly-separate login page.
Doesn't that mean the password manager is buggy?
Depends on how the fields are added/removed from the page, but if they're dynamically created (I don't think they are in this case) then they wouldn't exist at the document load time which is when the manager tends to fill in fields, to my knowledge.
While I can at least see the argument of form fields possibly being intrusive, it seems like a long stretch to me in this case. Were it a multi-field form collecting data, I get it, but for a login form on a site where 99% of the activity takes place behind that login it seems damn silly to me to hide it so much.
That’s pretty damn intrusive if the main purpose of your homepage isn’t even to provide you with the ability to log in. You obviously want to make it work with password managers but they should be able to pick it up. Mine can.
While hiding the respective fields on a homepage which has the main purpose of providing you with a login might not be such a good idea this is definitely so much better than any other solution which loads up a different page just to let you log in.