Any “Data goes crazy and takes over the ship” episode after the first one. You’d think they’d put in some safety protocols for dealing with that but just like clockwork, once a season, the Data Goes Crazy and Takes Over the Ship episode would come back. I think in the last season it happened twice…
Close follow up is any episode where ancient psuedo-mysticism is all powerful (a good example being that horrible Wesley episode mentioned above).
Another vote for Genesis.
When Riker is de evloving (is that a word? It ain’t science) into austropithicus-something, he gets phasered by Data. As he slides down the wall into unconciousness, Johnathan Frakes gives the finger.
They get tons of respect as we whoop it up every March on St. Patrick Stewart’s day, drinking Jim Bean-me-up and chanting baudy Klingon Limericks. What would we do without the Irish in space? There’d be a hell of a lot less transporter personnel, I can tell you that.
Code of Honor, the one where Tasha is kidnapped so as to become the leader’s wife, probably ranks right up there. Or down there. But, really, how bad can an episode be that has two women in skimpy outfits fighting to the death?
What about the one where Tasha gets killed by that black blob thing? It just seemed so… pointless.
Kasuo: They had to write her out somehow. ^:)^
The episode where Riker had a fling with a member of a monosexual species. Not only did it deliver a “message” about personal lifestyle choices with all the subtlety of a sledgehammer, but it made Riker look like a stupid horny jerk.
Like that’s hard to do. 
Yeah, that one was awful. It has my vote.
“Skin of Evil.” This one has my vote, too. Although the fact that it got rid of Tasha Yar means it has at least one redeeeming feature.
I was going to nominate that one, too. It was just so blatantly preachy. I mean, a lot of episodes had morals for us primitives, but that one was just, I don’t know, over the top somehow.
And all of the first season sucked.
If you’re talking about Brothers I must respectfully disagree, as it is one of the best episodes of the whole series. Not to mention that Brent Spiner carries about 2/3 of the episode himself, playing three different characters simultaneously.
Also, I liked A Fist Full of Datas, just for the sheer siliness of it. (Same reason I like The Royale, another much maligned ep.) I mean, Worf dressed up as a cowboy? It doesn’t get much better than that.
As for worst episode, I’d have to go with a tie between Genesis and anything that has Lwaxana in it.
Easy choice. Family.
The show got poor ratings and the ST:TNG producers, in their usual cluelessness, figured it was because there were no space battles, so they made sure from then on that there always were space battles.
But it wasn’t the lack of space battles. It was that, if you want to deal with human relationships (something ST was never very good at), your characters have to act like real human beings and you need writers who have something more than an fifth-grade knowledge of how emotions work.
There were three stories. The worst was Picard going home. It was sub-par soap opera, where fifty years of pain and resentment were magically cured by two minutes of mud wrestling. Rather sexist, too, when the two men tramp mud into the house and seem to expect the woman to clean up. And finally, we discover Picard grew up in France. We discover his brother grew up in France. Why the hell do they both have English accents?
Meanwhile, discover Worf has parents from the planet Schtick and Wesley gets to hear the usual ST cliched recorded validation from a dead person (i.e., “I’m dead, but don’t be sad about it because I’m taking it so nobly.”)
The only potential gem in this muck is the idea that Picard felt guilding about being taken by the Borg. Of course, that was never mentioned again. Also, if it’s bothering him as much as it shows in the episode, how the hell doesn’t their hotshot empathetic counselor notice or even consider the possibility?
Off the top of my head:
Naked Now - Crappy remake of a crappy TOS episode. Way too common in the first and second seasons. Bleh.
The Child - Troi gets impregnanted by a speck of light. Huh? Not that I’m jealous or anything…
Time Squared - Two Picards. I’ve blocked everything else from memory.
Remember Me - Crusher gets caught in a subspace bubble. I was a little dissapointed that she managed to get out.
Rascals - Children. Bleh. I hate children.
Phabtasms - Troi as a cake was nice but everything else in this episode gave me a headache.
Masks - Worst. Episode. EVER.
Oh, and everyone that said Below Decks and Genesis sucks. 
Those’re two of my favorite episodes along with Chain of Command Parts I and II, Parallels, Who Watches the Watchers, and that episode where Data crash lands on some planet and becomes the local Frankenstein.
hear hear, and Piscopo tells an ethnic joke! I thought they would be past that by their 24th century.
Yes, Masks was absolutely horrendous.
Some of them mentioned so far are pretty bad, but I absolutely hate “The Perfect Mate”, followed closely by “The Game”. Both were season five. Although season one had 26/26 bad episodes, I can’t bring myself to name any of them the worst.
The game. Oh yes, that fellates with great allacrity.
I’m just surprised that nobody’s mentioned the wretched “Cost of Living,” about which all that needs to be said is that Lwaxana Troi and Alexander get a great deal of screentime. Oh, and it has a mud bath sequence. Possibly two of them, iirc. Yargh.
Or, for that matter, the equally nauseating “Sub Rosa,” in which Dr. Crusher gets seduced by a “ghost” that’s actually some kind of plasma thingie. Spew.
And, of course, any episode featuring a Troi romance (this includes Troi/Worf UST as well as bland guest-stars-of-the-week).
BTW, I liked “Lower Decks,” too. And “Cause and Effect,” which is the one where the ship blows up over and over. That one’s fun.
Bad, really bad. Come on they were fighting each other to “death” with a cactus!
My votes for worst
The Royale: Aliens create world based on world’s worst novel, Producers create Episode based on world’s worst script.
Genesis: Part man, Part Spider…Mostly Wretched
46 minutes of Ashley Judd? Are you mental? 
BTW, I think the folks in Up the Long Ladder were actually Space Scottish.
–Cliffy