How to create an alias for a command in Vim?

To leave completion untouched, try using

cnoreabbrev W w

It will replace W in command line with w, but only if it is neither followed nor preceded by word character, so :W<CR> will be replaced with :w<CR>, but :Write won’t. (Note that this affects any commands that match, including ones that you might not expect. For example, the command :saveas W Z will be replaced by :saveas w Z, so be careful with this.)

Update

Here is how I would write it now:

cnoreabbrev <expr> W ((getcmdtype() is# ':' && getcmdline() is# 'W')?('w'):('W'))

As a function:

fun! SetupCommandAlias(from, to)
  exec 'cnoreabbrev <expr> '.a:from
        \ .' ((getcmdtype() is# ":" && getcmdline() is# "'.a:from.'")'
        \ .'? ("'.a:to.'") : ("'.a:from.'"))'
endfun
call SetupCommandAlias("W","w")

This checks that the command type is : and the command is W, so it’s safer than just cnoreabbrev W w.

With supplementary searching, I've found that someone asked nearly the same question as I.

:command <AliasName> <string of command to be aliased>

will do the trick.

Please be aware that, as Richo points out, the user command must begin with a capital letter.