There's lots and lots of debate here over which bits of Trek count and which bits don't. I often hear "I prefer to ignore [episode/movie/series X]" or words to that effect. I'm curious which bits of Star Trek fans prefer to pretend didn't happen. I personally take an all-inclusive approach, where every episode, movie, novel and comic combine into one gigantic tapestry, where the broad strokes jist of everything counts even if the specifics often don't add up (see video in my sig for a few examples of specifics not adding up!), and irrespective of if an episode or movie was any good or not. That said, Trip didn't die in "These Are the Voyages", that was just a shitty and inaccurate holodeck program
The lizard babies are out there. They are highly evolved and they are MAD. "Mommy.. why didn't you love us? Was it because Daddy was a twerp?"
The entirety of ENT. Basically every minute of Season 1 of TNG that isn't referenced in some way. TFF (continuity is honestly smoother without it between TVH and TUC). Just about every Borg ep in VOY after Scorpion, with little exception. All of those are very much in the "I try my hardest to ignore that they exist" list.
ENT-TATV- The only Star Trek episode that I will for sure never watch again. I ignore this episode while watching the series but also when rating season 4 as I don't think its fair to Manny Coto to let a horrible episode that he had nothing to do with bring down an otherwise outstanding season.
Picard being bald even when he was a cadet at the Academy. That's really the only thing for me, but even that I can explain away like so many other things in Trek.
I do not accept TATV. Seeing as how it was a holodeck episode then they obviously got it wrong. Anything to do with hologrpahic rights in VOY is also drivel. Though I am willing to accept that mutant human babies are out there somewhere in the DQ (why didn Voyager lock onto them and beam them aboard?). There are also many elements from Nemesis that are just plain wrong and must be ignored.
I count everything. But if I don't like it I just don't think about it much. I prefer to think of the stuff I like.
I count pretty much everything as well. Getting wrapped around the axle over something Trek is pretty much pointless (cue the diehards). I have been a Trekkie since the beginning and, frankly, haven't hated any of it. I've just gone along for the ride and taken it as it comes. Sure, I like some things better than others, but that pretty much goes for most things. No worries, though.
TATV? What's that? And what are these mutant lizard babies everyone's talking about? Is there a Trek series I don't know about or something? Seriously, I pretend lots of things didn't happen, such as the aforementioned episodes that shall not be named. Let's see...what else... I don't buy that the Prophets don't understand linear time. I prefer to think they were testing Sisko and trying to learn about how the human mind processes things. I think the same about the Q's claims of omnipotence, the idea that they have literally done everything that could possibly be done, and the idea that Q Junior was the first Q child ever. I prefer to think the Q have been lying every time they explained something to the humans. When I don't like something in Trek, I either ignore it outright or come up with a justification for it - something like "X isn't always true" or "he/she was lying/joking/wrong when he/she said that"...that works for things like Klingons being too tough to cook their food or to sleep on mattresses.
Enterprise doesn't count in my book It's hard to pick out of Voyager since so much of it was bad, but everyone knows which episodes were, so I will leave it up to the group. Star Trek the Abrams-verse (2009+): If they had left out the old universe and made their own, I might have gone along, but they had to pull old Spock into it and screw things up. The one thing I hated about Insurrection was the idea of "Manual Mode", like a star ship could be flown with a joystick, so Star Trek really IS nothing more than a video game! I didn't mind Nemesis (mostly) but I two things stuck in my head. The first was that Picard was a cue ball in star fleet, but he grew hair as he got older. Then data "came back" to torment the audience. I assumed Data's sacrifice was a message saying the actor wasn't coming back for another movie. To me they could have just killed Data off.
The Q were seriously overused in VOY. I was never all that fond of him/them in TNG and DS9 thankfully only had him once, but VOY just pushed it too far to the point where I am not ashamed to say I hate the Q. Holograms are tools, nothing more. What's next, tricorders going on strike? Granted VOY did get pretty weak, relying on a hot blonde with massive assests to save the show, but the one thing that bothers me with the series was that it never seemed challenging. One ship, 150-ish crew, lost and alone in a very hostile region (apparantly), but they never seem to have to struggle for resources, they shoot first and rarely even try to talk their way out of situations. I always think the series had potential, but it just missed all the targets that would have made it good.
I always imagine Riker saw a little sign that said, "While based on a true story, some events have been dramatised."
Most of Voyager, The Voyage Home, some of ENT, anything about prophets and pah-wraiths (DS9's records have been written to conform with the dogma, not what really happened), JJ Abrams' Star Wars.