I used to have a bit of software that would allow me to shrink films down to a box the size of a stamp in the corner of my screen so I could vaguely watch things while I'm doing animations and drawing. Since my hard drive died I've not been able to find another one that lets me do this.

What I want:

A resizeable player window
The window stays on top
The controls can be buried
The window doesn't have a minimum size
The window doesn't have large areas of black on it (the one I'm using currently always stays at 4:3 ratio even if the movie is in 16:9) which take up more space on the screen than needed.

That, to me, seems like a reasonable expectation, but I've not found it yet. The old software I used to use has been updated and now doesn't work the same way anymore. I miss having films on, but I don't want an eighth of my screen consumed by something that is basically unnecessary.

I've just had a fiddle with VLC (I'm using the Mac version but it's fair to expect that the Windows version has the same features):

A resizeable player window - yup
The window stays on top - yup, though you have to dig through a few preferences windows
The controls can be buried - yah
The window doesn't have a minimum size - Goes down to a box about the height of a postage stamp and 3 times the width (16:9 ratio) before limiting you
The window doesn't have large areas of black on it (the one I'm using currently always stays at 4:3 ratio even if the movie is in 16:9) which takes up more space on the screen than needed. - in windowed mode there are no black borders if the window aspect ratio is right, in fullscreen you can adjust the aspect ratio to get rid of the borders

Seconding the suggestion of VLC here. It's lighter that a helium balloon under favourable atmospheric conditions, and does the job well. It can cope with some pretty knackered files too.

I'll third VLC, I've been using it for quite a while now with no problems that I can recall!

also, it's nice to see Mr Fuzzy still alive - I guess he visits all the forum sections that I don't!

Huzzah! Thanks everyone. It's too late tonight to play with that, but I'll give it a go sometime in the next (rather busy) week. It sounds like just what I was looking for!