Let's be perfectly honest here. Code Geass has a very, very, VERY nasty habit of leaving cliffhangers at the end of every single episode, at least in the first season. The season is basically a 25-episode cliffhanger, ending with a scene that quite often leaves viewers screaming at the top of their lungs at their screens.
They also had a bad habit of the next episode beginning after the cliffhanger is resolved, and then drawing it out until a flashback shows how it actually ended.
And then comes the second season, where Every. Damn. Episode. Ends with a cliffhanger of cosmic proportions and every second one is a Wham Episode, to boot.
Parodied in the first episode of Magical Project S, which ends with the then-faceless Pixy Misa saying "you'll have to wait until next week to see who I am".
When D.N.Angel was put on a hiatus by its writer, fans were left hanging for two years in which Daisuke was setting off to find his kidnapped love interest's twin sister, and gets offered by his morally questionable rival for help. Fans were left waiting for two years until the manga was started up again and the arc was resolved.
After completing the aforementioned arc and even getting through another one, D.N.Angel is once again put on an at least six month hiatus with the completion of Part 1...with the massive cliffhanger of Riku finally seeing Daisuke (and Satoshi) transform, and asking if he's Daisuke...or Dark. And that's not even covering the stuff that still needs to be answered after that single chapter.
In True Tears, one of the driving factors for following the story asides the depth of the characters and the compelling love story are the constant cliff hangers on the end of each episode. Several of these tend to shake up things quite a bit.
Naruto is pretty infamous for this. One chapter even ended mid-sentence during such.
Bleach often ends with cliffhangers, especially when one character launches an attack against another. More often than not, the attack is non-fatal (and often, completely ineffective), and the next chapter shows why. If they are indeed fatal, then expect a flashback of the dying character instead.
Several episodes of Death Note, particularly the second-to-last one when Light has Mikami write all his enemies' names in the Death Note, end in cliffhangers.
Hayate the Combat Butler manga started out the current arc with one, and still hasn't resolved it. Leaving the fans to try and figure out how the pieces are going to connect. Doesn't help that the last arc gave us the starting of it, but leaving things vague enough for us to not realize that it was going to be left as a cliffhanger.
Zig-zagged in the anime adaptation of Berserk. The very first scene of the anime takes place a few weeks after the events of the Eclipse with Guts waiting for Godo to prepare the Dragonslayer. After the opening credits, the scene flashes two years later when Guts has a well-established reputation as the Black Swordsman. After defeating an apostle, the rest of the series reveals how Guts became the way he is in the present, starting with his first encounter with soon-to-be Big Bad Griffith. In the last episode, during the climax of the Eclipse, we see Guts screaming in rage and agony at the sight of the demon lord Femto raping Casca just as the credits role in. Although the very last scene reverts back to the very first scene, it is still left unclear as to how Guts managed to make it back from the hell dimension alive or whether Casca survived her ordeal and the viewers are still Left Hanging on this detail as Guts walks into the distance as the Black Swordsman, which is where the anime ends.
While the (classic) Pokemon anime has several multi-part episodes, its first series finale, denoted by the text "Next Time, A New Beginning!" instead of "To Be Continued...", qualifies. Ash is approaching Hoenn with his Pikachu taken sick as a side-effect of Team Rocket's latest capture attempt. Starting the next series in the following episode was likely done A: To emphasize May's role as the new Deuteragonist and B: to invoke this Trope, as Ash said his goodbyes to his Johto crew in the previous episode; it's just him and Pikachu to start this one off.
Every chapter has a Cliff Hanger in Bitter Virgin. The readers are even left hanging on the last chapter to how the relationship will end up.
The Giant Robo OVA ended on a great, gaping "To Be Continued". While the main conflict is resolved, it's implied that Big Fire still had a few more tricks up their sleeves.
Episodes 5 and 10 of Popotan: the former ends with Mai and Mea being left behind when their house jumps forward in time five years, the latter with Keith incapacitating Mea and making the house travel to its final destination.
The end of The Tower of Druaga: The Aegis of Uruk has Neeba and Kaaya abandoning their parties to climb up the heretofore unknown upper half of the tower. Even after the second season has started, no one knows what's going on with them and some of those left behind.
Except that later in the season, both parties team up and eventually catch up to them.
At the end of the first season of Sekirei, Minato manages to help Haruka and Kuno escape, which was the focus of the last portion of the season, but the Sekirei plan/battle has just begun, and the ending shows a bunch of loose ends which have yet to be resolved. The main Big Bad and game master even mentions the game is far from over. Fortunately Season 2 has arrived, and covers the next portion of the series.
So it is now a resolved cliffhanger?
The last episode of the English dub of Tokyo Mew Mew ended this way. Why? 4Kids was planning to continue it, but they didn't, due to "no merchandise tie-ins", possibly either due to companies not finding the concept of the show interesting, the molds for the Japanese versions of the toys not being able to find anywhere, or the most likely reason, Zakuro's weapon being de-crossed so it wouldn't offend non-Catholics.
The official reason is that 52 episodes was seen as too short by merchandise-companies. 4Kids would have had to have produced at least another season themselves.
Futari wa Pretty Cure MaX Heart has a cliffhanger in episode 5, when Cure Black and Cure White fought together with their new companion Shiny Luminous against Circulas. The battle just began. But the next episode starts in the next morning, Circulas was fine, the girls were fine, nobody knows what happened in this battle and how it ended. There were also no flashbacks.
At the end of the second episode of Mighty Space Miners, the mining colony on the asteroid Toutatis is in serious trouble: the accidental detonation of an orbiting nuclear warhead has sent Toutatis on a collision course with Earth, and instead of evacuating the colony, the Corrupt Corporate Executives on Earth who financed the enterprise have remotely activated another set of warheads they had previously hidden on Toutatis, which will destroy the asteroid and everyone on it in 36 hours. Only two episodes of this OVA were ever produced, and the cliffhanger is never resolved. (The eventual solution may have involved the miners ejecting the warheads into space in a specific direction and using their detonation to deflect Toutatis away from Earth.)
The Pokémon anime has a cliffhanger that was unresolved during the Best Wishes saga. The episode "A Venipede Stampede" led up to Team Rocket finding something linked to the Meteonite in the Desert Resort and Giovanni actually going there to claim it. The episodes that followed this were made, however, but the 2011 tsunami prevented the episodes from ever airing. In the dub, they even removed the cliffhanger at the end of the previous episode since it was apparent that the episodes after it weren't going to air. The final nail in the coffin came with Episode N much later, which retconned the two unaired episodes, and thus the 'hanger resolution, out of existence.