Manual:$wgDefaultSkin

Details
This setting sets the default skins>Special:MyLanguage/Manual:Skins|skin and should be set to the lowercase name of the skin (e.g. 'monobook', not 'MonoBook').

Note that this only sets the default skin. The site renders in this skin to anonymous visitors and to registered users who have not chosen a different skin in 1>Special:MyLanguage/Preferences|Preferences or temporarily overridden the skin. (Use  to limit the skins that users can choose in Preferences.)

Changing user preferences when removing a skin
In versions up to at most 1.11, upon registration the value of  was copied to the user preferences; thus setting $wgDefaultSkin to another skin would not have had any effect on registered users, even if they never changed their preferences. And it did not have an effect on registered users, who did change the skin to use.

When you remove a skin from the list of skins to choose from, use the maintenance script  to make sure that this skin is also not chosen by any user:

This will change the skin for all registered users, who have selected Monobook, to Vector.

Bundled
See Bundled extensions and skins.

Legacy information
Several skins are included with the MediaWiki installer tarball (the table below details the versions they were/are available with). You can find more skins in cat-skins>:Category:All skins|Category:All skins.

The first column gives the ID which should be used to configure this setting, the second gives the name as it appears within the MediaWiki interface and the third indicates the versions of MediaWiki that this skin is available for: