Enables tab to complete and cycle completions with company-mode, similar to neocomplete in vim

company-complete-cycle.el

;; Modify company so that tab and S-tab cycle through completions without
;; needing to hit enter.

(defvar-local company-simple-complete--previous-prefix nil)
(defvar-local company-simple-complete--before-complete-point nil)

(defun company-simple-complete-frontend (command)
  (when (or (eq command 'show)
            (and (eq command 'update)
                 (not (equal company-prefix company-simple-complete--previous-prefix))))
    (setq company-selection -1
          company-simple-complete--previous-prefix company-prefix
          company-simple-complete--before-complete-point nil)))

(defun company-simple-complete-next (&optional arg)
  (interactive "p")
  (company-select-next arg)
  (company-simple-complete//complete-selection-and-stay))

(defun company-simple-complete-previous (&optional arg)
  (interactive "p")
  (company-select-previous arg)
  (company-simple-complete//complete-selection-and-stay))

(defun company-simple-complete//complete-selection-and-stay ()
  (if (cdr company-candidates)
      (when (company-manual-begin)
        (when company-simple-complete--before-complete-point
          (delete-region company-simple-complete--before-complete-point (point)))
        (setq company-simple-complete--before-complete-point (point))
        (unless (eq company-selection -1)
          (company--insert-candidate (nth company-selection company-candidates)))
        (company-call-frontends 'update)
        (company-call-frontends 'post-command))
    (company-complete-selection)))

(defadvice company-set-selection (around allow-no-selection (selection &optional force-update))
  "Allow selection to be -1"
  (setq selection
        ;; TODO deal w/ wrap-around
        (if company-selection-wrap-around
            (mod selection company-candidates-length)
          (max -1 (min (1- company-candidates-length) selection))))
  (when (or force-update (not (equal selection company-selection)))
    (setq company-selection selection
          company-selection-changed t)
    (company-call-frontends 'update)))

(defadvice company-tooltip--lines-update-offset (before allow-no-selection (selection _num-lines _limit))
  "Allow selection to be -1"
  (when (eq selection -1)
    (ad-set-arg 0 0)))

(defadvice company-tooltip--simple-update-offset (before allow-no-selection (selection _num-lines limit))
  "Allow selection to be -1"
  (when (eq selection -1)
    (ad-set-arg 0 0)))

(with-eval-after-load 'company
  (define-key company-active-map [tab] 'company-simple-complete-next)
  (define-key company-active-map (kbd "TAB") 'company-simple-complete-next)
  (define-key company-active-map (kbd "<S-tab>") 'company-simple-complete-previous)
  (define-key company-active-map (kbd "RET") nil)
  (define-key company-active-map (kbd "<return>") nil)

  (put 'company-simple-complete-next 'company-keep t)
  (put 'company-simple-complete-previous 'company-keep t)
  (setq company-require-match nil)
  (ad-activate 'company-set-selection)
  (ad-activate 'company-tooltip--simple-update-offset)
  (ad-activate 'company-tooltip--lines-update-offset)
  (add-to-list 'company-frontends 'company-simple-complete-frontend))

(provide 'company-simple-complete)

company-mode/company-mode#343

Hey aaron, I did some modifications to your code to enable selecting options with arguments templates rather then just completing them (C-return and M-)
https://gist.github.com/kassick/845e4e59662a5b5c47f39bfd5941d31f

Hello @aaronjensen, thanks for the very useful snippet!
One problem I had is broken repeat functionality (dot) with evil-mode. To fix it:

(evil-declare-change-repeat 'company-simple-complete-next)
(evil-declare-change-repeat 'company-simple-complete-previous)