Kentaro Miura, the creator of Berserk, is practically legendary for this. When he is actually on schedule, new tankobon volumes of the manga come out roughly twice a year, not out of the ordinary considering the magazine it's published in, but he takes hiatuses a lot Ė most notoriously, he ended one hiatus to start another one just two months later. and Berserk is a chapter-a-month series. These breaks are likely necessary to stave off breakdowns.
D.Gray-Man has experienced several stops in production due to the author falling ill. After a hiatus in 2009, the series returned with a fifty page chapter... and another hiatus. However, from November on, it started running monthly rather than weekly.
Fist of the Blue Sky, the Prequel to Fist of the North Star can only enjoy sporadic and unannounced releases since 2005 due to Tetsuo Hara, its illustrator, becoming blind in one eye from a condition suffered by one in a million. Having lost depth perception, all his panels have to be re-drawn and inked by an assistant; the fact that his insisted style is realistic and intricately detailed does not help to alleviate the problem.
Hellsing: 10 years to finish a 10 volume manga. Kohta Hirano is (in)famously known for being quite a lazy mangaka when editors are not keeping constant watch on him. Near the end of the series it seemed Hirano would release a new chapter whenever he felt like it; he was often taking breaks from working in a monthly magazine. Many of the chapters in the second half of the series are just 9 to 12 pages long!
The OVAs also followed suit in what it seems to be a staple in the franchise, the first three episodes had just a few months between them (typical for a lavishly-animated OVA). From the 4th onward, the delays would just get longer and longer as Satelight was having a hard time producing the episodes all by themselves. After a year and half without releasing anything, Satelight passed the baton to Madhouse and it looked like they would keep up the pace, and they did... up to the 7th episode, another year and few months (and many rumors that Madhouse just dropped the series) is what it took for the 8th episode to get a release date; the series finally finished with the release of the 10th episode in late December 2012, nearly seven years after the series began.
At least the English release of the OVA's had an excuse (original licensor shut down during production of Episode 4; new licensor attempted to get the rest but a merger in Japan forced them to redo all the contracts from scratch, which took over two years).
Hirano topped himself with the prequel, Hellsing: The Dawn. After 6 chapters, he simply stopped in 2007. The Dawn didn't even have enough chapters to publish a single volume, so the series remains just a collection of 6 separate publications in 6 different Young King Ours+ issues.
Hunter ◊ Hunter, from the author of YuYu Hakusho, was featured regularly in Shonen Jump for several years. Nowadays the series is on hiatus much more than it is not, with roughly one collected volume coming out every year and a half or so (JC titles typically put out six or seven volumes in that same amount of time). Delays have been attributed to illness as well as the author and his wife spending time with their child.
Nausicaš of the Valley of the Wind was originally started in 1982 solely to get funding for the film (as people with money would not back an anime movie not based on a manga when Miyazaki was still a relative unknown). The final story was 7 volumes long (about 3Ĺ years for a monthly series, and these volumes were shorter than most), but it did not finish until 1994. This is because Miyazaki would take long hiatuses to directsomemoremovies. The end result of this is that the story in the Nausicaš movie only covers the first volume and a half of the manga.
The manga of Neon Genesis Evangelion had been running since just before the anime started and it finally reached its conclusion in 2013, after 18 years of production. It averaged around one 6-stage volume a year (that's about one chapter every two months). There could occasionally be a full year in between chapter releases.
Don't forget the Rebuild of Evangelion movies. The entire series was supposed to have finished up back in 2009. The current target release date for the final installment? "Winter 2015".
The second season of Haruhi Suzumiya: Announced back in 2007, said to be released fall 2007/spring 2008, eventually released summer 2009.
Don't forget the light novels. The first was released in June 2003 and the ninth and latest one was April 2007. As of this writing, they eventually released the tenth book and eleventh in May 2011. However, the eleventh novel was confirmed to not be the last volume.
The Descendants of Darkness manga began in 1997 and updated fairly regularly until the release of volume 11 in 2003. Then there was a full seven years between volume 11 and volume 12- it wasn't released until 2010 (apparently due to problems with author/artist Yoko Matsushita's health)
Due to Too Soon issues related to the Tohoku earthquake and tsunami of 2011, the penultimate episode of Puella Magi Madoka Magica was postponed. Word of God expressed relief at the delay, as the earthquake cost the staff precious time that would otherwise have been used to make the episode. Eventually it was announced that the last episodes of the anime would air together about a month later (although this was apparently well after the episodes were completed). The last volume of the manga adaptation and the Prequel manga Oriko Magica were also delayed, the latter being moved from April to May.
From the We-Couldn't-Make-This-Up department: JoJo's Bizarre Adventure had its 3rd arc licensed by Viz. It was scheduled to run over 16 volumes, which should've been a layup. The 11th volume was delayed from August 2008 to April 2009, eight months, and nearly derailed the entire run. Reason? Viz was dealing with protests from Moral Guardians about one panel in volume 10, Dio reading a book... which showed absolutely zero legible text. And why was this a problem? Because in the first anime adaptation, this page contains Arabic text. Yeah. That's it. Eight months lost to this.
Note that the actual manga series itself is from the We-Couldn't-Make-This-Up department but because of another reason. Hirohiko Araki, the writer and artist, has never missed a deadline in all 25 years of drawing Jojo (over 100 volumes and counting).
Mahou Sensei Negima!'s author, Ken Akamatsu, takes breaks lasting from a week to upwards of three weeks every now and then, claiming to be doing research. While he's almost as famous for his Shown Their Work moments as he is for inducing trope overdose, a lot of fans joke that his "research time" is spent researching his wife. In truth, as he has gotten older his drawing speed appears to have decreased and thus it takes slightly more than a week to draw one week's chapter, leading to a rough schedule of 3-4 chapters and then a break.
Akamatsu also took a lengthy hiatus about 3/4 of the way through Love Hina, so this isn't new territory for him.
Newer fans of Guyver tend to think this is what happens with Yoshiki Takaya however he consistently puts out one book a year and has never once put out an issue each month for an entire year. He did once have a hiatus to finish up another of his works from before Guyver.
One reason for the Adaptation Induced Plot Hole and somewhat abrupt ending of Fruits Basket's anime while the manga was still in progress? Natsuki Takaya, the creator, broke her left arm. Her drawing arm.note The other reason for the abrupt ending was that, because the anime was produced while she was recuperating, Takaya was able to be very involved in the anime's production. This resulted in a lot of micromanagement and meddling, which thoroughly pissed off director Akitaroh Daichi. Takaya didn't appreciate the pushback.
Digital Manga Publishing is infamous for this, as it can take years for them to release volumes. It's gotten to the point that many have assumed that they lost the licsenses when they actually haven't.