position: fixed doesn't work on iPad and iPhone
A lot of mobile browsers deliberately do not support position:fixed; on the grounds that fixed elements could get in the way on a small screen.
The Quirksmode.org site has a very good blog post that explains the problem: http://www.quirksmode.org/blog/archives/2010/12/the_fifth_posit.html
Also see this page for a compatibility chart showing which mobile browsers support position:fixed;: http://www.quirksmode.org/m/css.html
(but note that the mobile browser world is moving very quickly, so tables like this may not stay up-to-date for long!)
Update: iOS 5 and Android 4 are both reported to have position:fixed support now.
I tested iOS 5 myself in an Apple store today and can confirm that it does work with position fixed. There are issues with zooming in and panning around a fixed element though.
I found this compatibility table far more up to date and useful than the quirksmode one: http://caniuse.com/#search=fixed
It has up to date info on Android, Opera (mini and mobile) & iOS.
Fixed positioning doesn't work on iOS like it does on computers.
Imagine you have a sheet of paper (the webpage) under a magnifying glass(the viewport), if you move the magnifying glass and your eye, you see a different part of the page. This is how iOS works.
Now there is a sheet of clear plastic with a word on it, this sheet of plastic stays stationary no matter what (the position:fixed elements). So when you move the magnifying glass the fixed element appears to move.
Alternatively, instead of moving the magnifying glass, you move the paper (the webpage), keeping the sheet of plastic and magnifying glass still. In this case the word on the sheet of plastic will appear to stay fixed, and the rest of the content will appear to move (because it actually is) This is a traditional desktop browser.
So in iOS the viewport moves, in a traditional browser the webpage moves. In both cases the fixed elements stay still in reality; although on iOS the fixed elements appear to move.
The way to get around this, is to follow the last few paragraphs in this article
(basically disable scrolling altogether, have the content in a separate scrollable div (see the blue box at the top of the linked article), and the fixed element positioned absolutely)
"position:fixed" now works as you'd expect in iOS5.
position: fixed does work on android/iphone for vertical scrolling. But you need to make sure your meta tags are fully set. e.g
<meta name="viewport" content="width=device-width, height=device-height, initial-scale=1.0, user-scalable=0, minimum-scale=1.0, maximum-scale=1.0">
Also if you're planning on having the same page work on android pre 4.0, you need to set the top position also, or a small margin will be added for some reason.