CiviCRM Public APIs

The 'direction' that the APIS are going in is documented here. In general choose to use 'Create' rather than 'Add' and 'Get' rather than 'Search' to future proof your code

http://wiki.civicrm.org/confluence/display/CRM/API+Conventions

They are 5 different way of using the APIs:

as php function, for running your own code on the same server than the civicrm install
via the REST interface, can be called from another server via http calls
via the AJAX interface, to be called from javascript code
as Smarty function to add more variable not available by default in the template
using the CiviCRM drush module (in Drupal)

Most of the examples and API descriptions are using the syntax for the 1. (direct php call). However, all these APIs can be acessed via the other channels as well, provided you adapt the syntax (eg. the list of return variables is either a php array, several get parameters or a comma separated list).

API Overview

Scope and Definitions, Permissioning, Remote Invocation, Error Handling...

Using CiviCRM APIs - Code Snippets

Collection of code snippets which demonstrate use of CiviCRM APIs

Changes in CiviCRM 2

What's new in CiviCRM 2

Contact and Contact Search APIs

Create, update, find and delete contacts...

Contribution APIs

Create, update, get and delete CiviContribute contribution records...

Group APIs

Create groups, get members of groups, add and remove group members...

Activity APIs

Create, update, delete and get Activities

Location APIs

Relationship APIs

Create, retrieve supported relationship types (spouse, employer, etc.). Create, get, delete relationships between contacts (individuals, households and/or organizations...