Spoofed on Homestar Runner in the Strong Bad Email "cliffhangers", where Strong Bad is asked by a fan to "Resolve all the cliffhangers, please". After showing three mock cliffhangers, the email ends on an actual cliffhanger when Strong Bad's Lappy 486 computer gets stolen.
The online novel The Saga of Tuck has (for now) 142 chapters, each almost always ending on a cliff hanger.
At the end of THE GREATEST EVAR! by Matt Santoro, Hugo knocks Matt unconscious and takes over Matt's web series. This doesn't get resolved until the next episode, Drake NYC Riot!, when Matt gets his web series back.
The second episode (Mars Needs Moms) ends with one which got resolved with the third episode.
The ninth episode to the Postal review ended with one as well, which also got resolved with the 10th episode.
My Immortal ended just after Ebony had cast Avadra Keduvra (sic) at Voldemort, and we still don't know what happened after that since the author, Tara Gilesbie, was locked out by a Hacker, talk about Laser-Guided Karma...
Space Boyfriend ends in quite the famous one. Ben finally confesses his love to Veronica, and the series was canceled before she could respond.
Gotham: The Series  ends with Richard's mother, Elizabeth, attending the Nicole Miller fashion show and passing out leaving Catherine to call Richard to tell him that Elizabeth was rushed to the hospital. Elizabeth's fate is unknown. The series doesn't look like it's going to continue despite an Emmy nomination.
Return of the Cartoon Man ends with Roy and Valerie crossing into the Second Dimension to save Karen from Simon, along with a tease of Oswald Sherzikien's master plan, which supposedly affects the entire world. Expected to be resolved in the follow-up Journey of the Cartoon Man.
Dusk's Dawn: We never see what happened to the antagonist, or when the protagonists went to Celestia.
The newest episode of If the Emperor Had a Text-to-Speech Device ends with the Inquisition breaking into the Hall of the Golden Throne, only to be confronted by Magnus and mistaking him for a daemon. It remains to see how it'll be resolved.
The season finale of Brains has Alison grabbing her camera and running from the murderer Professor Sherman.