UltiSnips and YouCompleteMe

Another option is using the SuperTab plugin:

" if you use Vundle, load plugins:
Bundle 'ervandew/supertab'
Bundle 'Valloric/YouCompleteMe'
Bundle 'SirVer/ultisnips'

" make YCM compatible with UltiSnips (using supertab)
let g:ycm_key_list_select_completion = ['<C-n>', '<Down>']
let g:ycm_key_list_previous_completion = ['<C-p>', '<Up>']
let g:SuperTabDefaultCompletionType = '<C-n>'

" better key bindings for UltiSnipsExpandTrigger
let g:UltiSnipsExpandTrigger = "<tab>"
let g:UltiSnipsJumpForwardTrigger = "<tab>"
let g:UltiSnipsJumpBackwardTrigger = "<s-tab>"

Here YouCompleteMe is bound to a different combination Ctrln, but then that combination is bound to tab through SuperTab. UltiSnips and SuperTab play nice together, so you can then just bind UltiSnips to tab directly and everything will work out.

copy the following code to your vimrc, and enjoy. This function will handle all issues between YCM and UltiSnips.

function! g:UltiSnips_Complete()
    call UltiSnips#ExpandSnippet()
    if g:ulti_expand_res == 0
        if pumvisible()
            return "\<C-n>"
        else
            call UltiSnips#JumpForwards()
            if g:ulti_jump_forwards_res == 0
               return "\<TAB>"
            endif
        endif
    endif
    return ""
endfunction

au BufEnter * exec "inoremap <silent> " . g:UltiSnipsExpandTrigger . " <C-R>=g:UltiSnips_Complete()<cr>"
let g:UltiSnipsJumpForwardTrigger="<tab>"
let g:UltiSnipsListSnippets="<c-e>"
" this mapping Enter key to <C-y> to chose the current highlight item 
" and close the selection list, same as other IDEs.
" CONFLICT with some plugins like tpope/Endwise
inoremap <expr> <CR> pumvisible() ? "\<C-y>" : "\<C-g>u\<CR>"

i have this in my vimrc

"" YouCompleteMe
let g:ycm_key_list_previous_completion=['<Up>']

"" Ultisnips
let g:UltiSnipsExpandTrigger="<c-tab>"
let g:UltiSnipsListSnippets="<c-s-tab>"

thats what i did on my first try, but i misspelled UltiSnips with Ultisnips.. oh well, worked out in the end!

Try this suggestion on a page from the YouCompleteMe issue tracker. In your .vimrc:

let g:UltiSnipsExpandTrigger="<c-j>"

While this setting will make expanding a snippet share the default mapping for jumping forward within a snippet, it simulates TextMates' behavior as mentioned in the UltiSnips help tags.

Since I've mapped my Caps Lock key to Ctrl, this mapping works pretty smoothly.