According to the Adult Fans of Lego (AFOLs), LEGO had one from about 1997-2002 during the advent of "juniorizaton". Sets from that era were generally simpler and more crude than previously, using large, single-purpose parts as opposed to more complex subassemblies. Examples include Town Jr. and City Center (which replaced the regular Town line) — the cars were made of single-piece baseplates, and the headlights were usually just slopes with headlight texture printed on them (as opposed to using "washing machine" bricks with transparent plates on them). Castles were also simplified by using premade wall pieces. The era also had many poorly-received series, such as the Insectoids and the Time Twisters. However, starting in 2002 the situation started to become better - by 2005 the new City line was a complete antithesis to Town Jr.
LEGO's "Constraction" subline (Slizers, BIONICLE, Ben 10, Hero Factory) arguably also went though such a period from '06-'10, beginning with the introduction of the "Inika" body-build, named after the Toa Inika sub-line of Bionicle, which basically consisted of an easily buildable torso with snap-on limbs, each made up of very few pieces. This type of construction hiked with the '08 Matoran, '09 Agori and '10 Ben 10 sets, figures whose torsos, upper and lower arms and legs (or in the Matoran and Agori's case, their entire limbs), hands and feet were made up of huge, single pieces and offered very little in the way of construction, focusing more on being "just" action figures.
The Hero Factory 2.0 line in '11 thankfully ended this dork age with its radical design overhaul, that, although gave up on using the traditional LEGO Technic pin and rod connectors, made its figures pleasingly complex and incredibly well articulated again. Needless to say, though fans were generally happy, they were disappointed to find that this shift was so groundbreaking, it's bound to stay for a while, threatening with the notion of an "Inika 2.0".
When it comes to LEGO, the name Galidor is used as a synonym for failure. The theme was backed by a huge promotional push (TV show, games, McDonald's promo) and comprised a line of "standard" action figures with interchangeable limbs, which is where the construction part ended. While the toys weren't bad for average action figures, the series was met with scorn for doing away with LEGO's traditional building system and utilizing extremely specialized parts, and is considered to be their biggest bomb.
My Little Pony's toy line suffered this in the late '90s, when Generation 2 came along. They scrapped their previous chubby designs in exchange for a design that resembled horses instead of ponies. Generation 2 only lasted 1 year in most places. It was the only one that never got any sort of Animated Adaptation.
Another, short lived dork age occurred in 2009 with the G3.5 toy line, which limited the ponies to just seven characters alone (dubbed the "Core 7") and changed their designs to having large heads and hooves, but small bodies. The Core 7 was barely tolerated when it still had the typical G3 design, though fans were left with a sour taste as many ponies (including the Ensemble Darkhorses that are Minty and Star Catcher) were shoved aside and personalities were changed for the remaining ponies, but the redesign is really when the Dork Age set in. This awkward period ended in October 2010 when Hasbro switched to Lauren Faust's designs for My Little Pony: Friendship Is Magic, although your mileage may vary with the Generation 4 toys...
G.I. Joe arguably had its Dork Age in the early-mid '90s, when the line introduced more outlandish subsets like the Eco Warriors (basically, G.I. Joe meets Captain Planet), Ninja Force, and Street Fighter (no really!). Not helping was the decidedly bright and blatantly neon coloring for certain figures, as well as the overabundance of spring-loaded weaponry, among other gimmicks. Plus, there was the added competition from lines like Teenage Mutant Ninja Turtles and the coming of a certain morphenomenon, all of which spelled the end for the "Real American Hero" line by 1994. This was followed by a rather short dork age in the form the Sgt. Savage line, which introduced a Captain America-esque soldiernote the eponymous Savage didn't dress in red, white and blue, but his origins shared a lot in common with Cap's, including the Super Soldier angle, as well as being frozen for an innumerable amount of years. helping the Joes against new enemies, but the line was short-lived.
And following on Sgt. Savage was G.I. Joe Extreme, where the toys had Liefeldian proportions and designs and articulation was reduced down to five points. While Sgt. Savage changed the scale somewhat it still kept most of the traditional Joe articulation and sculpting style intact, while Extreme was a blatant Follow the Leader to The Dark Age of Comic Books.
The franchise took another major hit in the 2000s with G.I. Joe: Sigma 6. The idea was to reduce the massive number of Joes down to a small, more characterized group (the eponymous "Sigma 6") and could have easily done well as a reboot if not for the decision to take a design turn towards Animesque as well as largely discarding the eclectic uniforms of the characters for fairly bland sci-fi jumpsuits. Later, Hasbro would try the concept again with G.I. Joe: Renegades, getting slightly better results but not by much.