For a series that was originally conceived at least partly Edutainment series for a family audience, Doctor Who, especially in the new series, has snuck a few past the TV code (for the most part, these are from the 2005-present revival series; the original 1963-89 series tended to attract more concern about violence than innuendo).
WARNING! THERE MAY BE UNMARKED SPOILERS!
The Hartnell years could give the New Series a run for its money in the sex department.
In "An Unearthly Child", Ian suspects Susan might be sneaking into the Junkyard to "see a boy" (innocent enough out of context, but bear in mind she's sneaking into an abandoned Junkyard in the middle of the night, suggesting that Ian thinks she's got more than holding hands in mind).
A jailer in "The Reign of Terror" pretty much offers to let Barbara go in return for sex. Thankfully she doesn't oblige.
Barbara was almost raped again in "The Romans", this time by Emperor Nero.
Edith is raped off-screen in "The Time Meddler", as confirmed by Verity Lambert on the DVD commentary. She also explains why the Hartnell era had a higher concentration of sex references; while social taboos were stricter due to the recent introduction of TV, there was less in the way of strict rules on content. There was more of a general consensus on what was appropriate for broadcast, and whether you breached it came down mostly to the whim of the producer.
This little gem from "The Myth Makers": "Upon my soul, you're making me as nervous as a Baccante at her first orgy." Steven Moffat at least tries to disguise his dirty jokes.
Captain Avery: What makes you think I'm the kind of man who likes the company of gentlemen, sir? The Doctor: Why, your dress, your tastes...
The Italian soldier in "The Tenth Planet" has Page Three Stunna posters on his wall and pornographic mags around his bunk.
In "The Chase", Ian is implied to habitually engage in some rather conservative crossdressing:
Ian: Oh, er, Barbara, could, I, er, have your cardigan?
Barbara: Oh, not again.
Ian: It's for the Dalek, not for me.
"The Doctor Dances": the Doctor discusses "dancing" with Rose, a little miffed that she assumed he'd never "danced" before. He has, it's just been a while. Later, when the Doctor and Rose are dancing note the literal kind of dancing in front of Jack, Rose assumes that Jack wants to cut in and dance with her. As it turns out, he'd rather "dance" with the Doctor.
"Dalek": Viewers were apparently so upset over a reference (in a sexual context) to "spooning" (lodging a number of complaints) they appeared to miss the fact one of the characters in this episode utters the strong (even for 2005) swear word "goddamn," which as of 2013 remains the strongest word uttered in the main Doctor Who series (for stronger language, you need to watch Torchwood). That may be dependent on your location — in the UK and in Australia, neither "damn" nor "goddamn" are really considered swearwords.
Cassandra: She's back! Oh, that little blonde bi— (cut to the Doctor and Rose talking) Rose: Bit rich, coming from you. [...] —>Cassandra: That portion of skin came from the front of my body. This... came from the back. Rose: Right, so you're literally talking out of your ar— Cassandra: Ask not. [...] Cassandra: (in the Doctor's body) I'm a man! So many parts... and hardly used. (significant look at Rose)
In the mini-special "Time Crash", The Tenth Doctor mentions to the Fifth Doctor (their TARDISes intersected when Ten was redecorating) that the Master was running about again. Five asks whether or not the Master "still had that rubbish beard." Ten responds that no, but he does have a wife.
The 1920s porn that Colonel Curbishley secretly looks at in "The Unicorn and the Wasp". That got more questions from the kids than the gay relationship in the episode.
"The Eleventh Hour" has The Doctor run into a man he met earlier to use his laptop. When he snatches the computer away and looks at it he says "Blimey! Get a girlfriend!" — and later on: "Delete your internet history". Bravo Moff.
Okay, who here actually believes that Amy shows up to parties in skimpy outfits to kiss people? Hey, a kissogram is actually a thing, costumes and all. They're just a bit... quaint. And hence fitting for Leadsworth.
And in "Flesh and Stone", there was the scene in Amy's bedroom. How the hell did they get away with that?!
There was a hilarious example in "The Vampires of Venice", in which Rory pulls out a tiny light to ward off the vampires with. In response, the Doctor immediately pulls out a massive ultraviolet bar. Cue:
Rory: Yours is bigger than mine. The Doctor: Let's not go there.
"Oooh, Doctor, you sonicked her..." To make this even more remarkable, that's her daughter she's talking about. Although she and the audience don't know that yet.
And in "Vincent and the Doctor" the monster seems to rather enjoy one of the sonic settings. The monster even returns the favor by repeatedly bumping a door that Eleven is leaning against. Eleven has a visible reaction.
In "A Christmas Carol", Amy and Rory are wearing their policewoman and Roman costume throughout the whole episode (having just had their honeymoon interrupted), and always change the subject when someone brings their clothes up.
Rory: You know, history lesson, a bit of fun every now and then, a bit of nostalgia!
Rory: Heh... no. Why do I get slapped? The Doctor: Because we have to stick to the established chain of events. One mistake and the whole timeline could collapse. We'd end up with two Amy Ponds forever, and then what would you do? (Rory looks at Amy with raised eyebrows) Amy: (gasp; slap)
The Doctor: (regarding his and River's destination) You could read a book by [the stars]. River: (suggestively) Is it okay if I don't? The Doctor: We've got ten minutes, so get dressed. River: Oh, that's so close to the perfect sentence. The Doctor: Hmm.
A bit later...
The Doctor: (referring to the diary) From now on, there are rules. River: Ooh, Doctor, you've got all strict — not that I mind.
From "Last Night":
(the Doctor is trying to resuscitate a Future!River, who's playing dead, and then—) The Doctor: River... you are holding your breath. River: You're a fine one to talk about holding. How many hands do you have?
The Doctor: River, you can't do things like that! River: Or what?[...] What else are you gonna do, spank me?
(yet another River enters the TARDIS, followed by her Doctor) Future!River: (sees Present!Doctor) Two of you! The mindraces, does it not? (Future!River and Future!Doctor leave, just as Present!River returns) Present!River: (seeing Future!Doctor) Two of you! The mindraces, does it not?
With none of this taking into account a certain dress.
In the 2011 Christmas Special "The Doctor, the Widow and the Wardrobe", there is a scene where, in order to save a planet full of sentient alien trees, the tile widow, Madge, takes the collective "souls" of the trees inside herself. During this process, she seems to be having an orgasm.
Doctor Who is classified as a children's/family show. "The Time Monster" has the Master on Earth making a teleporter that pushes matter through time and space called "Transmission of Matter Through Insterstitial Time". They even use the abbreviation TOMTIT. One investor gets mad at the expense and that the machine doesn't seem to work properly. "Even the name is offensive! tomTIT", with an emphasis on the last three letters. And STILL nobody in the censor board noticed.
In Britain, "tit" also refers to chickadees (which are actually a mostly old world family anyway). And that's the definition that the word tomtit is based off.
It's also Cockney rhyming slang for, well, exactly what you think.
The Series 6 trailer had a naked River, though anything cleavage-based wasn't seen. The scene was cut from the final episode.
"Handcuffs! Why do you always have handcuffs?" Followed by "You. Me. Handcuffs. Must it always end this way?"
There is plenty to be scandalized by in the classic serials, too. I mean, come on! For those of you who can't play the video, Four is attempting to communicate with a large alien and presses his face against a suspiciously phallic-looking appendage.
The Doctor: I don't know, but I can't feel my feet... And other parts. Rory: I think all my parts are basically fine. The Doctor: Stop competing.
Also in that episode, the Dream Lord says to Amy "The Doctor left you alone with me. Anything can happen." And as he says those last two lines he transforms into wearing basically a bathrobe and has a very creepy expression on his face.
"Asylum of the Daleks" has, at the end of the episode, Amy and Rory — their relationship repaired — standing outside their house. Amy gives Rory a steamy look and walks inside. He smiles for a second, fist pumps, and follows her.
"Pond Life" part two has one combined with a noodle incident — The Doctor bursts into Amy and Rory's bedroom, only to immediately cover his eyes and yell at them to "stop what [they're] doing!" They were only sleeping, but considering they also have a rule about the Doctor bursting into the bedroom...
Amy was probably wearing either a bra or lingerie under the sheets, as she's clearly hiding her breasts while Rory allows his plain, blue T-shirt to be seen.
Also, at the end, Rory says, "I really hate it when he does that," suggesting that the Doctor has walked in on them more than once.
Melody Malone and her "cleavage that could fell an ox at twenty feet." The Doctor's clearly enjoying himself reading too, given the "Yowza!" It's really not so bad considering it's River Song and therefore his wife. On the other hand, he's reading it in front of her mother, and River herself wrote it.
According to the behind-the-scenes publication The Doctor Who Companion: The Eleventh Doctor Vol. 6, the original script would have had the Doctor utter the phrase "Traffic was a bitch." Evidently either Steven Moffat or the powers that be thought better of this and changed the dialogue.
River has a subtle Showing Off the New Body moment in "Let's Kill Hitler" when she walks offscreen for a few seconds to (it's heavily implied) check out her new body's butt in a mirror. We only hear her shrieking in delight, and later promising that she's "going to wear lots of jodhpurs!" Because it happens offscreen, it's not blatant enough to count as outright Fanservice. And the joke is only obvious if you know what jodhpurs are. Even moreso, when you consider that she's wearing a loose-fitting dress in that scene — meaning that she'd have to have deliberately lifted up her dress to get a good look at her bottom. Which would be way too saucy to show on-screen on an episode of Doctor Who.
The made-for-DVD minisode "Clara and the TARDIS" has Clara conducting a surprisingly frank conversation with the TARDIS about whether she's the first girl the Doctor has had, ahem, stay the night. The TARDIS' subsequent slideshow of past female companions (with Clara taking particular notice of Amy's legs) leaves it unclear — from Clara's point of view — as to whether or not these were actually past romances of the Doctor. To her credit, she seems to take this lengthy "girlfriends list" in stride. One wonders about her reaction had the TARDIS chosen to also display images of Adric, Harry Sullivan or Captain Jack.
A virtually identical gag was used in an Amy minisode where she makes the TARDIS display images of the former companions, taunts the Doctor about it, and gets a Head-Tiltingly Kinky reaction to a woman in a "leather bikini" (a reference to Fourth Doctor Nubile Savage companion Leela).