Now, if I could travel through time, I'd head for the future, but for some reason, people just keep heading for the not-so-distant past where they run into their own mothers.
1. Your mother falls for you.
When Marty McFly heads back to the Fifties in Back to the Future, I'm fairly certain winning his mother's affections wasn't on his to-do list, especially since he needs her to fall in love with his father in order to be, you know, born in the first place. Also because it's his own mother. It's bad enough as a teenager to have to contemplate your parent's love life; the last thing you really want is to become a participant. And Marty McFly might be a lot of things, but he isn't the guy from Reason #2, who . . .
2. You fall for your own mother.
Sure, Oedipus did it, but we all know how well that went. So when Lazarus Long, the protagonist of Robert A. Heinlein's Time Enough for Love, finds himself doing just that, he should have an inkling it's a bad move. Long accidentally jumps into 1916 when he'd been aiming for the Twenties, and he falls in love with his own mother. In order to avoid the object of his affections, Long enlists in the army and ends up a combat soldier in World War One. (Un)fortunately, he survives and returns to consummate his love. Awkward. (Basically, he manages to end up fighting in war that he didn't really want to and still manages to do his own mother. This makes a strong case against time travel right here.)
(2B. You are your own mother: Heinlein also wrote the short story titled "—All You Zombies—" in which the protagonist somehow manages to be both his own mother and his own father due to a lot of relatively convoluted circumstances, including emergency sex changes and baby-stealing. Thus convincing me that sexual relations and time travel do not mix.)
3. Your mother thinks you're having an affair with your father.
Actually, "Father's Day" (Series 1, Episode 8 of Doctor Who) gives out a whole laundry list of reasons you should never voluntarily go back in time to meet your parents. Rose wants to be there for her father, Pete, on the day he dies, but when she saves him, she seriously messes up time and Reapers (flying creature who eat temporal paradoxes for lunch—literally) descend. When she and her father meet up with her mother, her mother, Jackie, assumes Rose to be her husband's hot young mistress. Rose's father explains that, no, Rose is his daughter, and Jackie reads it as one of those "Surprise! I have a secret lovechild from my dark secret past" things, à la an episode of As the World Turns. Pete hands Rose her baby self, but Rose having physical contact with another her causes further paradoxing. (Perhaps an addendum to the rules of time travel should be, "Don't touch yourself.") Actually, this whole situation is starting to sound like a soap opera. But with paradox-eating monsters.
4. You disappoint your mother and she doesn't even know who you are.
In Episode 4 of Life on Mars (UK), Sam Tyler, still stuck back in 1973, runs into his own mother, Ruth, while trying to take down a gangster named Stephen Warren that has half the police force in his pocket. Warren even tried to pay off Sam, who takes the money very, very reluctantly. When he learns that his mother's having money trouble, he tries to alleviate his guilt by offering her the money. She is, of course, offended, additionally reading him as one of those dirty bribe-taking cops. Lucky for Sam, she has no idea he's her son, so her opinion of Sam Tyler hasn't been lowered any. Just her opinion of a cop she thinks is named Bolan. (Who knew that Sam was a glam rock fan? Additional note: In the equivalent episode of the US remake, Sam's mother is named Rose. That's right. Rose Tyler.)
5. Dramatic Irony
In "In the Beginning" (Supernatural, Season 4, Episode 3), the angel Castiel (who I notice dresses exactly like Loomis from the original Halloween film) sends Dean Winchester back in time to 1973, telling him to "stop it." Stop what? He really doesn't say. And I'm noticing that 1973 seems a popular year to meet your parents. Anyway, Dean meets his father, John, and basically tells him which car to buy, before running in to his mother and learning that (Surprise!) she comes from a family of hunters, and (Surprise! Irony!) it's a lifestyle she would never wish on her own future children. Which is, of course, part of the appeal of John: he's not a hunter, just a nice, normal guy. Again with the dramatic irony. Anyway, by the end of the episode, she's made a deal with the Yellow-Eyed Demon that seals Sam's demon baby fate (and her own doom) in exchange for John's (nice, normal, non-hunter) life. After which, Castiel shows up and tells Dean he couldn't have stopped that from happening anyway. He just told Dean to try in order to prove that you can't. Methinks Castiel needs to find less jerktastic ways of proving his points. But, hey, at least Dean got an experience that O. Henry probably couldn't have written better.
6. Your mother-daughter meet-up becomes a bad after-school special. Literally.
In 1977, Francine Pascal of Sweet Valley fame wrote Hangin' Out with Cici, a Young Adult novel that tells the tale of an adolescent girl named Victoria who thinks that her mother is too strict and doesn't understand her. Clearly, her mother has no idea what it's like being thirteen. One day, however, she finds herself suddenly in the past, where she meets a cool girl named Cici, who's apparently the most awesome new friend Victoria could have asked for. It's no surprise, then, that Cici is Victoria's mother, who does in fact know what being thirteen is like. Touching, right? So touching, in fact, that in 1981, it was made into an ABC Afterschool Special, entitled My Mother Was Never a Kid. I figure the lesson was supposed to be something touching about parental relationships, but what it really teaches you is that time travel can happen anytime, anywhere, without warning or reason.