This SMBC webcomic.
This is the first one I thought of. The second I thought of was Making Mr. Right.
If webcomics count, there’s www.dieselsweeties.com; I mean it’s right there in the name, and everything.
Yeah, but he’s a robot too, so it doesn’t count [ducking and running]
In the book version of the Stepford Wives:
Most of the men had been living with their robot wives, some for years. No, I don’t know why I bothered to spoiler box such an old and well-used story. I didn’t see the movie version that came out a few years ago.
Also, in an episode of Buffy the Vampire Slayer Warren had been dating a robot for some time before dumping her for a flesh woman. In a later episode, the robot is recycled to look like Buffy and Spike has a relationship with it.
“The Tin You Love to Touch” by Robert Bloch
The Twilight Zone episode The Lonely featured Jack Warden in love with a robot played by Jean Marsh.
Terminator: The Sarah Connor Chronicles never quite got there but it was obvious John Connor had some wood for Cameron’s metal. I wish they had addressed it more directly on the show because they had the best tension, much better than that other girl they tried to pair him up with.
TSCC also had a plot in which a Terminator replaces a married man and carries on the relationship. The wife knows something is wrong but they end up doing all the things married people do right up until the Terminator kills her.
Terminator Salvation was headed that way too but the scene was cut. Originally, Marcus and Blair were supposed to STAF- Sit Tight And Fuck.
In the classic 1981 film Heavy Metal, the story So Beautiful And So Dangerous depicts a sexual and romantic relationship between a robot and Gloria.
Ray Bradbury’s short story Marionettes, Inc. is about a couple of guys who purchase android versions of themselves so they don’t have to spend time with their wives. One finds out his wife has purchased her own Marionette. Hijinks ensue.
I keep thinking about this theme, because it seems to me I’ve read tons of stories that feature this, but it’s hard to remember them all with my books packed away.
There was a very old television show called My Living Doll in which was about an Air Force captain who was given charge of a female android played by Julie Newmar. Yeah, that Julie Newmar, catwoman Julie Newmar. I never saw an episode of it, but considered it was a TV show in the 50s with Julie Newmar as a female robot, I bet it set records for skeeviness of all kinds.
Robert Cummings, I believe, was the AF Captain.
Because I’m an asshole, I’ll talk about TV and comic books!
There’s two popular girly manga that fit the bill.
Absolute Boyfriend by Yuu Watase has specially designed robot boyfriends. This is Japan, of course, where the more quirky members of society can already get body pillows and life-size dolls, so exploring full on androids is just another step. Anyway, the heroine gets a free sample boyfriend or some shit I can’t remember and she loves how perfect the boyfriend is. After all, he was designed for the sole purpose of romance! Insert wacky hijinx and the heroine finally choosing a real, flesh-and-blood boyfriend instead of a robot.
Chobits by CLAMP has a dude finding an irresistibly cute and pedobait female android named Chi who has been thrown into the trash. Chi is special, because unlike all those other lame robots, she’s been programmed to feel emotion! And her on switch is located, of course, right in her nether region. The entire thing is like an awkward college student who has never had sex, whether or not dated, suddenly having his own personal hot teenage girl to take advantage of. As you can probably tell, I’m not overly fond of the series. 
In one of my favorite books, He, She, It, the protagonist Shira falls in love with the cyborg Yod.