The WordPress current user information is available through this global variable. It is an instance of class
WP_User defined in [wp root folder]/wp-includes/capabilities.php. It is set in the pluggable function
set_current_user($id, $name='') and
get_currentuserinfo() in [wp root folder]/wp-includes/pluggable-functions.php.
WP_User has methods for role and capabilities of the user.
WP_User($id, $name = ''): the constructor, it can be used to instantiate a user with specific user ID.
get_role_caps(): gets capabilities
add_role($role): adds specified role to the user
remove_role($role): removes specified role
set_role($role): sets role
level_reduction($max, $item): reduces level
update_user_level_from_caps(): translates from capabilities to user levels
add_cap($cap, $grant = true): adds capabilities
remove_cap($cap): removes capabilities
has_cap($cap): queries for a specific capability
translate_level_to_cap($level): translates from level to capabilities
User ID of the current user can be accessed using $current_user->id field. Profile information of the current user can be obtained by using by using the member variable $current_user->data, but other global variables are available like $user_login, $user_level, $user_ID, $user_email, $user_url, $user_pass_md5 and $user_identity for this information.
Plugin and theme authors can use this global variable to get information about the current user. Most commonly required information would be about what the current user can do. WordPress provides the function
current_user_can($capability) for finding out capabilities of the user. The different capabilities are the different actions a user can take, they are:
As mentioned by Mark Jaquith in the comments, level_* are deprecated and are available only for backward compatibility. New plugins and themes should not use them. The methods concerned with levels should also be avoided.
There are some more functions available like user_can_edit_post and similar, but they are deprecated. current_user_can should be used instead of these.
Back to full list of global variables.