Animation Age Ghetto: The studio's relationship to this trope is... complicated, to say the least. Their sense of snarky humor and broad appeal have brought in legions of adult fans, but their films are almost always conceived and marketed for younger audiences. Even the relatively more "mature" films like Shrek and How to Train Your Dragon are clearly meant to be family-friendly. This reputation (as well as their failed attempt at prime time television) has labeled CGI as mostly kiddie fare.
The fans who wish they would do traditional animation again, even some who want them to be exclusively traditional, versus those who prefer their All-CGI Cartoon works.
The sale of the studio to NBCUniversal. While some in the media biz, including some of NBCUniversal's own competitors (particularly Viacom), praised the sale as a well-organized strategy to take on Disney, others, particularly animators, historians, animation fans and amateurs, fretted over a hypothetical Seasonal Rot of DreamWorks' future projects under their new owners. This is especially evident with the Hype Backlash Universal's Despicable Me received years prior due to the oversaturation of the Minions in pop culture. The news that Illumination Entertainment head Chris Meledandri, who produced Despicable Me, would replace Katzenberg as DWA CEO after the sale was completed only added to the division given his mixed record in animation production. On the financial side, some analysts criticized the $3.8 billion price tag as overpriced, believing that Comcast could never recoup the money it paid for the studio due to the studio's dwindling value even if NBCUniversal took DWA's intellectual property and milked it to the fullest potential. Then there are those who feel the deal was a sellout and that NBCUniversal should have paid more; one of DWA's shareholders on this side sued Katzenberg, alleging he made a side deal to benefit himself while leaving minority shareholders in the dust.
Cash Cow Franchise: DreamWorks Animation was unique among animation studios at the time of its creation for being a studio dedicated entirely to turning every single one of their successful films into franchises, rather than (like Disney and Pixar) creating a series of one-off films. Every American animation studio created since DreamWorks - Blue Sky Studios, Sony Pictures Animation, Illumination Entertainment, etc. - have picked up this approach, and even Disney and Pixar have loosened their "no theatrical sequels, ever" policy because of it (the success of Wreck-It Ralph and Frozen also contributed to this mentality for Disney/Pixar).
This is because DWA, as opposed to it's rivals, was a publicly traded company, which means that if a movie bombs or is sucessful, DWA loses money and must layoff people, or the shareholders ask for sequels, while it's rivals are owned by big studios and thus have no problem with underperforming films.
Stillborn Franchise: The unfortunate flip side of this approach of course means that every original DreamWorks film that bombs or disappoints at the box office will automatically become this.
Ensemble Darkhorse: Puss in Boots was an extremely popular character with audiences in the Shrek series, so he got his own movie. And a TV seriesnote It's a Netflix exclusive in the US, but DWA is airing it on it's newly launched channel in Asia (where Netflix doesn't exist in most countries), so it counts. In a similar vein, the penguins from Madagascar got their own TV series and got their own movie too.
Follow the Leader: Earlier on in their history, before they decided to go in a "light fantasy" direction to counter Pixar's more "epic" films, they were notorious for copying the template of whatever Pixar film was being developed at the same time.
While DreamWorks were copying Pixar, everyone else was copying DreamWorks (Disney even joined the fray for a few movies). Shrek in 2001 was followed by numerous imitators, and its template pretty much defined what "animated fairy tale" meant for the rest of the decade. And that's not to mention the number of copycat studios that were created after DreamWorks proved that non-Disney feature animation could be profitable, a few of which are still around today.
Friendly Fandoms: Some of The New Ten's DWA films such as How To Train Your Dragon have seen their fanbases on good terms with a few Disney fandoms (it helps that the directors of Dragon also did Lilo & Stitch.)
It sometimes seems as though they grow their beard out when they feel like it. They started with one with the very mature religious epic The Prince of Egypt, then shaved it off when they started making forgettable Shrek clones, and eventually re-grew it in The New '10s with more mature films like How to Train Your Dragon and Kung Fu Panda. However, due to their bloated production schedule of both types of films, Turbo and Home being released in-between the former's sequels see them regularly jump back and fourth between respectable and schlock.
Harsher in Hindsight: In October 2015, Jeffrey Katzenberg was involved in a car accident that destroyed his Tesla car and hospitalized him with a broken arm. The Harsher in Hindsight trope comes into play when one realizes that this is nearly 10 years after Pixar/Disney animator Joe Ranft died in a car crash, which was 20 years after a valuable member of Disney's Nine Old Men, Wolfgang "Woolie" Reithermann, passed away in a car crash himself.
They've gotten plenty of flack for being a part of a fixed income scandal with other major animation studios including Pixar and Blue Sky but it has yet to sully their name or the other two studios' names, so it's averted so far.
The infamy that Katzenberg and the studio got for creating films like Antz and Shark Tale, which didn't endear them to Disney or a handful of other people, never really went away and dragged on DWA all the way up to the sale to Comcast/Universal.
Periphery Demographic: Their brand of snarky, in-your-face humor has earned them plenty of adult fans, to the point that they're accused of doing it on purpose.
"Seinfeld" Is Unfunny: When Dreamworks first went into producing their own animated films, they did so under the belief of being an alternative to Disney. Movies like Antz and The Prince of Egypt dealt with more "adult" topics that were then uncommon for Disney to cover. The unexpected success of Shrek, which was praised for its witty humor, good use of Celebrity Voice Actors, and ability to appeal to multiple age groups, as well as the decline of traditional animation led Dreamworks to try and duplicate its success with their future films. Unfortunately, this led to every other animation studio not named Pixar copying their schtick, including Disney with Chicken Little. Suddenly, Dreamworks went from being the innovator of Western Animation films to being the representation of everything wrong with it. This Forbes Article actually goes quite in depth with it.
On PDI's end, the morphing technique that they pioneered in the late 1980s became overused by the early 1990s.
Throw It In!: A few of the background jokes (like the "Utah Teapot") in "Homer3" were added in by the companynote the left-handed "X, Y, Z" signpost actually corresponded with PDI's software at the time.
Uncanny Valley: Some of their human designs suffer from this for having exaggerated features but realistic surface textures. Though arguably, it's not as bad as when they had all of their characters be an Ink-Suit Actor.
Visual Effects of Awesome: If not in story quality, Dreamworks definitely matches up to, if not outright surpasses at times, Pixar in this department.
What Could Have Been: PDI (pre-Dreamworks) had plans for a feature-length CGI movie as early as 1985. It never happened due to money issues.
Win Back the Crowd: The Kung Fu Panda sequence of Master Oogway's death up till Po's despairing confession to Master Shifu about his deep self-loathing that the old Red Panda feels helpless to counter. In that sequence, Dreamworks Animation showed that it had recovered from its post-Shrek 2 creative nadir that drove away its partner, Aardman Animations, and learned how to make stories with profound emotional depth with a skill rivaling Pixar. That in turn made the blistering wuxia action to follow all the more powerful when you have grown to care about these characters.
How to Train Your Dragon, natch. If you're talking about single sequences of extraordinary emotional power, you can't go past 'Forbidden Friendship', the epic battle against the Red Death, and Hiccup waking up after the battle and discovering he's lost his foot.