Special features compared to other wiki software (see also http://wikipedia.sourceforge.net/features.html ):
Side bar A bar on the left or right of the screen with short-cuts
Skins Different ways to present the site.
File upload feature allows to upload graphics or sound files, see special:Upload. Uploaded files are listed on RecentChanges and they are also logged on log:Uploads.
Watchlist Every page has a link "Watch this article for me". Use special:Watchlist to track changes on the articles you declared an interest in; watched articles are also bolded in the Recent changes list .
Namespaces Separated from the page name with a colon.
Automatic signature Just type three times ~ when you edit, and on saving the page, it will be replaced with your user name and a link to your user page. If you use four tildes, the current date will be added as well. Mainly intended for Talk pages.
Word-extension linking If you include a link of the form [[war]]s, or [[war]]time, the system will automatically display it as if you had typed [[war|wars]] or [[war|wartime]], respectively, saving some typing.
Parenthetical hiding If you include a link of the form [[kernel (mathematics)|]], the parenthetical portion will be hidden in the link: kernel. This is useful for disambiguating different meanings of a word without making linking too difficult or cluttering up the text of articles. This also works with cropping out namespaces when you want a cleaner-looking link: [[Wikipedia:copyrights|]] becomes copyrights
User contributions At the top of each user page, there is a link to display a list of all articles the user has worked on, according to the database.
Interlanguage links: handy method for linking articles between the versions of Wikipedia in various languages.
Side-by-side diffs - the diffs are shown side-by-side, and changed portions of lines are highlighted, making it much easier to see what's what. Additionally, a diff is shown during an edit conflict so you can see exactly what you need to reintegrate.
Math: see texvc
Features that some wikis support but MediaWiki does not:
CamelCase: By using a word with MixedCase, you do not automatically create a link.
The main Wikipedia software currently has the following functionality (basic wiki features not listed):
Database-driven (MySQL, no other databases currently supported), persistent connections
Smart caching: rendered pages are saved as static HTML files and served as such unless modified
Translated into many languages (see Multilingual coordination on Wikipedia for details)
Editing syntax based on UseMod, with support for mixing wiki-syntax and HTML. Only free links are supported for linking, not CamelCase (deliberate design decision).
Support for mathematical formulas using LaTeX. These are rendered as HTML, PNG or LaTeX source depending on user preferences.
"Pipe trick" 1: [[foo (bar)|]] becomes a link to "foo (bar)" displayed as "foo" (the text in parentheses is not shown)
"Pipe trick" 2: [[User:Foo|]] becomes a link to "User:Foo" displayed as "Foo".
Full text search; "Go" button allows direct viewing of a specified article's contents (tries near match if no exact hit)
Edit preview (can be shown before or after edit box)
Basic support for handling edit conflicts (page being saved by a user while still being edited by another one, then saved again)
Cookie-based account and login system, but anonymous users can also edit pages.
"Skins": Using object-oriented programming, the main design can be inherited into other classes, and different themes can be designed relatively easily. Currently three skins are part of the default distribution.
Basic privilege scheme: sysops can protect and delete pages, edit protected pages, ban users, run SQL queries on the database.
All revisions of an article are stored (currently uncompressed). Diffs between two revisions can be generated.
Pages can be deleted and undeleted.
Pages can be moved (renamed) by signed in users.
Every signed in user can add articles to their "watchlist". This watchlist then shows changes made to these articles recently. Users can have all their edits watched by default.
Edits can be marked as minor; users can decide to hide such edits from the Recent Changes list. Only signed in users can mark edits as minor.
"What links here": View pages that link to the current page (backlinks)
"Related changes": View a filtered version of Recent Changes to the pages linked from the current page.
Contribution lists show the edits made by a user. From there, sysops can also easily rollback (revert) edits by an individual user.
Message notification (user gets a "You have new messages" notice if someone else has edited his user discussion page); this also works for anonymous users
Support for subpages (link to "Foo/Bar" from "Foo" by just typing "/Foo", "Foo/Bar" contains a backlink to "Foo"), these can be enabled or disabled by namespace (e.g., Wikipedia currently supports subpages on discussion pages, to make archiving easy, and on user pages, to give users space for personal pages)
Namespaces allow content separation (to address the namespace, use the [[Namespace:Page title]] syntax). Discussion pages are separate from article pages, "meta" project pages can be separated from content pages, image pages are used for image descriptions.
Uploading and embedding of any file type is possible.
"Stub" threshold: Users can see links to articles below a certain size rendered in a different color
Users can enable an option that allows them to edit individual sections of an article (separated by headlines) instead of loading the entire article.
Users can enable an option that allows them to edit articles by double clicking them.
Random article function
Support for automagically turning ISBN numbers into links to an editable list of booksellers
Special report pages:
New pages: List of newly created articles
Ancient pages: Articles sorted by timestamp, ascending
List of images
List of users
Orphaned articles (articles that have no links pointing to them)
Popular articles (articles by number of visitss, works only if counters are enabled)
Most wanted articles (non-existent articles sorted by number of links pointing to them)
List of all pages by title
Support for signing comments on discussing pages
Support for auto-numbering headings in an article, and/or generating a table of contents for long articles
Support for linking to individual sections of an article
Users can configure their timezone, which is used on all report timestamps
The attributes of many report pages (number of results etc.) can be set in the user preferences
Support for emailing users through the wiki (email address not shown to the user)
Printable versions of articles can be generated
InterWiki link support (e.g. MeatBall:SoftSecurity becomes http://www.usemod.com/cgi-bin/mb.pl?SoftSecurity)
Interlanguage link support (only if multiple wikis are set up)
Better interlanguage link handling through a single table for all wikis
Article category support
Improved image handling
More granular user privileges