I\'ve tried different sites/products and this seems to be split fairly evenly. Windows 7 and Gmail allow you to insert spaces in your password. Hotmail and Twitter do not.>
The main problem I see would be usability for the user in terms of e.g. trailing spaces. Also if you start allowing non-visible characters like the space you might also start allowing all sorts of other non-visible characters like tabs and so on. Imho the disadvantages outweigh the benefits. To make a password really secure just increase the length and allow some special characters, numbers and letters and be case specific. With e.g. > 20 digits thats practically unbreakable at this stage (at least in terms of worth the effort..).