There are 40 modules in Drupal 7 "Core".  They are located at:

DRUPAL_ROOT/modules

The modules are listed here, in alphabetical order.  

Announcements feed module (announcements_feed)

Aggregator module (aggregator)

Block module (block)

Blog module (blog)

Book module (book)

Color module (color)

Comment module (comment)

Contact module (contact)

Contextual links module (contextual) [Drupal 8 Contextual links Documentation]

Content Translation module (translation)

Dashboard module (dashboard)

Dblog module (dblog)

Field module (field)

Field SQL Storage module (field_sql_storage) **

Field UI module (field_ui)

File module (file)

Filter module (filter)

Forum module (forum)

Help module (help) Drupal 8 Help module

Image module (image)

List module (list)*

Locale module (locale)

Menu module  (menu)

Node module (node)

Number module (number) **

OpenID module (openid)

Overlay module (overlay)

Path module (path)

PHP filter module (php)

Poll module (poll)

Profile module (profile)

RDF module (rdf)

Search module (search)

Shortcut module (shortcut)

Statistics module (statistics)

Syslog module (syslog)

System module (system)

Taxonomy module (taxonomy)

Testing module (simpletest)

Toolbar module (toolbar)

Tracker module (tracker)

Trigger module (trigger)

Update module (update)

User module (user)

XML-RPC module (DRUPAL_ROOT/xmlrpc.php -> DRUPAL_ROOT/includes/xmlrpc.inc)

* Drupal 8 Documentation (Drupal 7 documentation appears unavailable)

* Sub-module of Field module