Too many to list individually, but they tried to get away with as many innuendos and double entendres in each episode as possible. Kevin Murphy is on record saying that basically the writers wanted both kids and adults to laugh at the same jokes, but for different reasons.
The Satellite of Love is familiarly referred to as the "SOL" (a well-known acronym for Shit Outta Luck... which could also fairly describe Joel's/Mike's/Jonah's position).
In The Crawling Eye, Joel asks the bots what they think of the movie. They start talking about human heads and what happens with them, when...
Crow: I was listening to the scientists, and they said you had your head up your a—
Joel: *Covers Crow's mouth with his hands*
In The Hellcats, a film with a frankly alarming number of jets of beer foam flying around, Crow repeatedly remarks "I hope that's beer."
In a host segment of Godzilla vs. Megalon, Crow and Tom were looking at some photos with great interest and hide them from Joel.
Joel's riff from Pod People: "Trumpy felt scarred by his ugly hillbilly...nose." A reference to a notorious bit from Albert Goldman's controversial 1981 biography of Elvis Presley. note "Like most country boys of his time, [Elvis] wasn't circumcised. A sensitive adolescent at heart, he saw his beauty disfigured by an ugly hillbilly pecker."
In The Amazing Colossal Man, when the title appears, Crow snarks, "Oh, yeah, you wish!" Then there's this line when Glenn's fiance Joyce is talking to him.
Servo:(as Joyce) I'm still looking forward to our honeymoon!
The writers oftentimes say things like "You can get away saying certain things with a puppet that you couldn't with a person". Notably Crow's "I wanna decide who lives and who dies!" line from Santa Claus Conquers the Martians.
The riffs where the police chief refers to people not wanting to "kiss his bird" in Bride of the Monster.
The lyrics to "Tubular Boobular" exploit the fact that while certain words would be censored, nonsense words that sound just like them can slip through - provided you use about fifty of them.
It's an arealogical, autoerotical, tubular boobular joy!
An exposular-regional, batchical-pouchular fun for girl and boy!
A latissimal-dorsical, hung-like-a-horsical, callipyligical ball...
Outlaw Of Gor is full of butt puns throughout. And Servo and Crow about to comment on a phallic statue before Mike stops them. They still get away with "I was just going to say I envy that structure..."
In Santa Claus, Santa has a bunch of "technologically-advanced" devices including the Tele Talker, which is a mouth on the wall that speaks things that people are saying across the globe. It looks so questionable, though, that Tom even wonders, "I hope those are lips."
Subverted in the opening for Bloodlust, where Gypsy attempts to circumvent the censor, and accidentally invokes the word she was trying to insinuate.
Gypsy:[Regarding Pearl] Oh, I'm tempted to call her something that rhymes with "bitch" - Oh! I said it!
Bots: She said it! Gypsy's in trouble, Gypsy's in trouble!
In the short Why Study Industrial Arts, a quick shot of a construction worker hammering at an unidentified object between his legs inspires the riff: "I can't get this thing back in my pants, Earl!"
During the letter reading segment of The Starfighters, during the "refueling scene", Crow sticks his beak up Servo's hoverskirt. Servo gasps for a moment, then clearly enjoys it.
Since Once Upon a Honeymoon is about a songwriter forced to work before leaving on his honeymoon, the short is filled with these.
Crow: Let's see... What rhymes with "blue balls?"
Mike: What would Liberace do?... Oh, I better not do that.
Laserblast has an instance not from the riff, but from the film itself. One of the cops says "shit" at one point near the beginning of the film, and despite the volume being lowered in an attempt to mute it out for the show, the word can still be made out.
When Tom Servo blocks the hull breach with his hoverskirt, he starts giggling uncontrollably as the vacuum of space sucks at him from underneath, declaring, "I'm experiencing a sensation altogether new to me and frankly, I love it!" When Mike removes him, he growls, "Aw, darn!"
The riffs during a scene involving runaway truck rigs on a hill in Riding With Death, non-stop sexual double-entendres that get more blatant and dirtier with each riff ("Mah rigid grill structure is bearing down on yer unprotected cargo door."), culminating in Crow's line, "My oft-complimented Peterbilt is rhythmically nudging yer sweet honey pot—" which leads Mike to put the kibosh on the whole thing.
Which of course, leads to this:
Mike: "Drained and satisfied, I'm tracin' lazy circles on yer supercab now..." Crow: And you said I was bad. Mike: Well, you inspired me.
Along with the above, Servo shouts "She's PREGNANT?!" after the main heroine announces she's late.
Kevin Murphy's ancient-Roman character whom the Pearl-era Mads accidentally drop in on is named Callipygeas. This isn't a Latin name, it's Greek — and it means "one who has a nice arse".
Before Invasion of the Neptune Men, Pearl is heckled by a Roman citizen because of her lack of popularity in comparison to Bobo, to which Pearl quickly replies, "Slut - I mean, what?"
The Projected Man has a truly volatile one: the lead female actress says "You can't, Chris!" and Servo remarks, "WHOA! What'd she call him?" Say her quote aloud to yourself in a thick British accent to get the joke.
Not to mention a direct mention of the Kama Sutra after a detective states that he's seen a dead acquaintance "in a great number of positions before, but nothing quite like this!"
Geri's mother: I just don't want you to be disappointed if he doesn't come.
Crow (as Geri): Mother, that's private.
Jonah states if he's given a space suit he'll need one with more room in the "groinological area". From the bots reaction, it's pretty clear what he's implying and it's not about his height.
In Yongary, a newlywed couple is called into work just as they were about to go to bed. The wife gives the phone's antenna a frustrated shove back in, and Jonah makes fully explicit what was likely intended as a Visual Pun even in the film itself: "That's a metaphor for our honeymoon."