Webisode

Mini-episode of a broadcast or cable series, available online or by other new media.

Examples of Webisode include:

Anime

Azumanga Daioh has a short web chapter that looks like Chiyo recording her class with a camcorder.
Haruhi-chan, a super-deformed Self-Parody of Suzumiya Haruhi.

The Animatrix previews that were released online to hype the release of The Matrix Reloaded.

Between seasons 3 and 4, Lost created a series of 13 mobisodes, dubbed "Missing Pieces," which were delivered to cell phones, then posted online.
Heroes issued a webseries, "Going Postal" between seasons 2 and 3.
The new Battlestar Galactica has done this twice, with a series before S3 called "Resistance" and a set of webisodes on the Razor DVD which correspond to the First Cylon War.
Doctor Who had them for its second new series. They were called TARDISODES.
- The "prequels" for series six episodes also qualify.
MythBusters does this.
The Office has them.
The Critic was briefly revived as a web series.
Season 8 of Scrubs had a video-blog by Sunny Day, one of the new interns.
The Chloe Chronicles, which tied into seasons 2 and 5 of Smallville.
Breaking Bad has done them ever since season 2 began. Most of them are far Lighter and Softer than the show.
Have I Got News for You tried it, but seemed hamstrung by the fact that most of the airtime was taken up all the contestants laughing at how ridiculous the word "webisode" was.
Community
Parks and Recreation
The Walking Dead
Kung Fu 3D
The Engine Sentai Go-onger and Kamen Rider Kiva net movies, used as tie-ins for The Movie. While Super Sentai hasn't really used them since (except for Super Hero Taisen), they've become a staple for Kamen Rider—and are frequent sources for the funniest moments in the franchise.