If you don't want to do omnicompletion or don't have the latest vim, try adding this to your .vimrc instead.

function! TabOrCompletion()
    let col = col('.') - 1
    if col==0 || getline('.')[col - 1] !~ '\k'
        return "\<TAB>"
    else
        return "\<C-N>"
    endif
endfunction

inoremap <tab> <c-r>=TabOrCompletion()<cr>
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