I wanted to have a single key stroke that would save existing files, or call the file browser.

Here's a key map for Ctrl-S to accomplish that (place in vimrc file):

if has("gui_running")
  " If the current buffer has never been saved, it will have no name,
  " call the file browser to save it, otherwise just save it.
  :map <silent> <C-S> :if expand("%") == ""<CR>:browse confirm w<CR>:else<CR>:confirm w<CR>:endif<CR>
endif

Comments

Recommend an imap for the same functionality so one can hit ctrl-s without having to make sure one isn't in insert mode:

:imap <c-s> <Esc><c-s>

If one prefers to return to insert mode after the save, the following mapping may be used instead:

:imap <c-s> <c-o><c-s>

Has the nice advantage of allowing one to save in the middle of typing. (I actually have two different keys mapped, one for each of the two above behaviours.)

I use:

 imap <c-s> <c-o><c-s><CR>

So that the confirmation doesn't hold you up.

mswin.vim (included with GVim 6.2 for windows) defines:

" Use CTRL-S for saving, also in Insert mode
noremap <C-S> :update<CR>
vnoremap <C-S> <C-C>:update<CR>
inoremap <C-S> <C-O>:update<CR>

To enable mswin.vim in vim 7+, just add the following to your .vimrc:

source $VIMRUNTIME/mswin.vim