As pointed out by paldepind, isearch-forward-symbol-at-point (M-s., by default) is a close equivalent to * in Vim. This function is available starting in GNU Emacs 24.4; if your Emacs is different or older, read on for alternatives.

Usually I just do (M-b ...) C-s C-w ... C-s. That is:

1. M-b to move to beginning of word(s) of interest
   • zero or more of these
2. C-s to start an I-Search
3. C-w to yank the word(s) starting at point
   • one or more of these
4. C-s to find the next match
5. more C-s to find later matches
6. RET to exit the I-search at the most recent match
   • or a bunch of C-g to abort back to the original starting location

Here is a go at integrating it into I-Search (invoked via C-s and C-r; use C-h k C-s for info on isearch).

(require "thingatpt")
(require "isearch")
(define-key isearch-mode-map (kbd "C-*")
  (lambda ()
    "Reset current isearch to a word-mode search of the word under point."
    (interactive)
    (setq isearch-word t
          isearch-string ""
          isearch-message "")
    (isearch-yank-string (word-at-point))))

Integrating it into I-Search takes advantage of its word matching and case sensitivity settings (C-s M-c C-* would do a case-sensitive search on the word under point).

Try C-sC-w

Here is a start:

(global-set-key (kbd "C-*")
  (lambda ()
    (interactive)
    (re-search-forward (format "\b%s\b" (thing-at-point  word)))))

These days there is also Smart Scan, a lightweight add-on package that provides this functionality.

It is available from MELPA; instructions for adding MELPA to the list of enabled package-archives are here.

To install it:

M-x package-install RET smartscan RET

You can then enable it via

(global-smartscan-mode t) ;; Turn on Smart Scan globally

The default key bindings for searching forward and backward are M-n and M-p, respectively.

PS: If you are interested, the original blog post introducing this package is here.

if you re using viper (which works great) this should work similarly enough:

(require  thingatpt)
(require  viper)

(defun viper-search-word-at-point ()
  "Reset viper-s-string to word at point and start a forward viper search."
    (interactive)
    (setq viper-s-string (word-at-point))
    (viper-search viper-s-string  t nil))

(global-set-key (kbd "C-*")  viper-search-word-at-point)

C-s C-w is ok but it s not strictly symbol search, but "word part at the right of point" search.

The correct answer is M-s . This starts symbol search with the symbol at point preloaded. Symbol search is a special mode of isearch that you can start with M-s _. If you re already in isearch (for example, after pressing C-s or C-r) you can also type M-s _ to enter symbol search.

I urge you to read the entire documentation of isearch since it s very powerful and versatile.