Let's take a look.

GORMENGHAST: Intended to be a 10-book series, but an episodic one based around Titus's continuing adventures. In this context, TITUS ALONE and GORMENGHAST are a duology (focusing on Steerpike's attempt to seize control of the castle) and TITUS ALONE and probably AWAKES are episodic. However, they continue Titus's character development from the first two books. Therefore, arguable.

FOUNDATION: Asimov's plan was to chronicle the 1,000-year history of the Foundation from the fall of the First Galactic Empire to the Second, and this story is covered throughout the books. So definitely a continuous series, and less than half-finished upon his death. ROBOTS is also part of this structure.

PERN: Episodic sub-series and stand-alones, so not a serialised story.

MIDDLE-EARTH: Debatable, as mentioned above. THE SILMARILLION acts as a prequel to HOBBIT and LotR, and Tolkien considered them thematically parts of a larger whole, to the point where at one stage he refused to publish LotR without THE SILMARILLION as he considered them indivisible. I think most would disagree with that, but THE SILMARILLION adds context and understanding to subsequent readings of LotR.

SHANNARA: Several sub-series, though linked by the story of generations of Ohmsfords. Arguably the first seven and maybe FIRST KING can be said to be one big story, possibly the GENESIS/WORD & VOID stuff another.

DYING EARTH: Books 1 and 4 are semi-standalone, but Books 2 and 3 are one story separated by a lengthy publishing gap (19 years).

RINGWORLD: Haven't read anything other than RINGWORLD, so no idea.

RIFTWAR: There are divergent stand-alone side-novels, but Feist has said he considers the whole thing to be the story of Pug and the Five Great Riftwars, which began in MAGICIAN and ends in 2013 with MAGICIAN'S DESTINY.

EARTH'S CHILDREN: Continuous series.

ODYSSEY: 2001 and 2010 are arguably heavily interlinked (2010 answers questions left unanswered in the original), whilst 2061 and 3001 are cheesy additions to the series. Technically not a continuous series then.

WAR AGAINST THE CHTORR: Continuous series.
AMTRAK WARS: Continuous series.
DISCWORLD: Mostly stand-alone stories.
WILD CARDS: Up until the most recent batch, a continuous series. The newer books take a 'Next Generation' approach, arguably beginning a sequel or sub-series.
DEVERRY CYCLE: Continuous series.
DARK TOWER: Continuous series.
WHEEL OF TIME: Continous series.
AMBER: Continuous series (or rather two continuous series which form a larger whole).
RAMA: First book was a stand alone with a deliberately ambiguous ending, but the latter three form a continuous series (with additional stand-alones in the same universe).
OZ: Episodic adventures.

I should have added David Brin's UPLIFT SAGA (29 years, 6 books left on a large number of unanswered questions with a promise that more books were supposed to follow) to the list as well.

David Wingrove's CHUNG KUO series is one that would be interesting to debate: Book 1 came out in 1989 and the final book written the way Wingrove planned won't be out until 2015. However, the 'first draft' of the series was given an ending (if not a particularly good one) in 1998 and there is now a 'second draft' of the series consisting of the original books rewritten and a number of new books which began in 2011 and will end in 2015. So that can be argued.