Add this to your .vimrc:

autocmd FileType python set omnifunc=pythoncomplete#Complete
autocmd FileType javascript set omnifunc=javascriptcomplete#CompleteJS
autocmd FileType html set omnifunc=htmlcomplete#CompleteTags
autocmd FileType css set omnifunc=csscomplete#CompleteCSS
autocmd FileType xml set omnifunc=xmlcomplete#CompleteTags
autocmd FileType php set omnifunc=phpcomplete#CompletePHP
autocmd FileType c set omnifunc=ccomplete#Complete

Try it out:

$ touch index.html
$ vim index.html
type: <ht[CTRL-X][CTRL-O]