Times when #StarTrek
has been deadly serious, a thread:

When the Emergency Medical Hologram decided to (briefly) pursue a singing career in Voyager's "Virtuoso".
When Q turned the crew of the Enterprise-D into characters from Robin Hood in The Next Generation's "QPid"
When a misfit band of Ferengi try to rescue Quark's mother from the Dominion, end up killing their own prisoner by mistake and generally make fools of themselves (also with a cameo by Iggy Pop) in DS9's "The Magnificent Ferengi"
When Picard, Ro Laren, Guinan and Keiko were turned into children in The Next Generation's "Rascals", which was kind of a cute episode.
Scanning for life forms in Generations.
When Quark became Lumba in an effort to restore Zek to the status of Grand Nagus in DS9's worst episode "Profit and Lace"
Poor Beverley falls in love with a ghost in The Next Generation's "Sub Rosa" and reads a 'particularly erotic' part of her grandmother's diary.
(Also Marty McFly and Darth Vader are clearly seen on gravestones).
(Also Marty McFly and Darth Vader are clearly seen on gravestones).
Travelling through time to 1986 in a stolen Klingon Bird of Prey to rescue Earth from a probe that's been sent to talk to humpback whales by getting some whales and transporting them to the future in Star Trek IV
Don't go criticising her counselling technique, warns a drunk Deanna in First Contact.
The crew of the Enterprise rush to save the Captain's dog Porthos who contracted a deadly virus only to find out the aliens to who have a cure won't help because Porthos pissed in a sacred tree in "A Night in Sickbay."
The prolific use of Space Nazis when the writers have run out of ideas for a new bad guy and just go "sod it, slap them in an SS uniform and make the holodeck go wrong"... or time travel.
Sisko challenges a racist Vulcan to a baseball match and loses the game but succombs to his human need for emotion and gets drunk with his mates at Quark anyway in DS9's "Take Me Out To The Holosuite"