How to automatically install Emacs packages by specifying a list of package names?

; list the packages you want
(setq package-list '(package1 package2))

; list the repositories containing them
(setq package-archives '(("elpa" . "http://tromey.com/elpa/")
                         ("gnu" . "http://elpa.gnu.org/packages/")
                         ("marmalade" . "http://marmalade-repo.org/packages/")))

; activate all the packages (in particular autoloads)
(package-initialize)

; fetch the list of packages available 
(unless package-archive-contents
  (package-refresh-contents))

; install the missing packages
(dolist (package package-list)
  (unless (package-installed-p package)
    (package-install package)))

Based on comments by Profpatsch and answers below:

(defun ensure-package-installed (&rest packages)
  "Assure every package is installed, ask for installation if it’s not.

Return a list of installed packages or nil for every skipped package."
  (mapcar
   (lambda (package)
     ;; (package-installed-p 'evil)
     (if (package-installed-p package)
         nil
       (if (y-or-n-p (format "Package %s is missing. Install it? " package))
           (package-install package)
         package)))
   packages))

;; make sure to have downloaded archive description.
;; Or use package-archive-contents as suggested by Nicolas Dudebout
(or (file-exists-p package-user-dir)
    (package-refresh-contents))

(ensure-package-installed 'iedit 'magit) ;  --> (nil nil) if iedit and magit are already installed

;; activate installed packages
(package-initialize)

Emacs 25.1+ will automatically keep track of user-installed packages in the customizable package-selected-packages variable. package-install will update the customize variable, and you can install all selected packages with the package-install-selected-packages function.

Another convenient advantage of this approach is that you can use package-autoremove to automatically remove packages that are not included in package-selected-packages (though it will preserve dependencies).

(package-initialize)
(unless package-archive-contents
  (package-refresh-contents))
(package-install-selected-packages)

Source: http://endlessparentheses.com/new-in-package-el-in-emacs-25-1-user-selected-packages.html