Need examples? Okay...
Phantom of the Opera - I was asked my opinion on this the other day and I responded that aside from my limited tolerance for people singing about EVERYTHING, I'm not a big fan. See, murdering stalkers who are given to rape and kidnapping aren't really my type. I'm weird like that.
Enrique Iglesias "Escape" - "You can run, you can hide but you can't escape my love" Really? Huh. I could have sworn that was called stalking and I'm pretty sure it's illegal.
Twilight - Oh, don't look at me like that. You knew it would come up. The guy watches her while she sleeps and gets angry when she sees people he doesn't like, just for starters. He's a stalker and a douche of a boyfriend. In real life this shit is NOT ROMANTIC. It's abusive. And the chick is such a classic victim it makes me want to vomit blood. Young women should NOT think that this shit is a good thing! This is shit they teach you in recovering from abuse that you should see as a red flag. It actually concerns the shit out of me that Stephanie Meyer is sending this message to girls and apparently believes it's okay.
James Bond (every movie) - Long live the god of "No means yes and more no means 'kiss me'." I actually like James Bond but the way he treats women has always annoyed the shit out of me. Kirk has this same problem in Star Trek, the idea that women really just want to be bossed around and treated like sex toys. That when we say no, a good smack and forcing a kiss will make us understand that the man was right all along. Again, not romantic. Abusive, yes. Sexual harassment, yes. Total dickwadish, absolutely. Romantic, not even a little.
Aerosmith "I don't wanna miss a thing" - This would be really sweet and romantic if it weren't so incredibly creepy. These are about the clingiest, neediest, obsessive lyrics ever written. If you had a boyfriend this insane you'd be trying to get a restraining order.
Say Anything - Calling someone 8 times in a row and showing up at their house with a boombox to serenade them? Intensely creepy. John Cusack is the only person who should ever, ever, ever attempt this maneuver.
The Police "I'll be watching you" - I almost didn't include this because it's actually a song about a stalker. Then someone reminded me that there are still people who use this song for wedding first dances and other applications that would seem to imply they have no idea that this shit is wrong. Once more people, say it with me - STALKING IS NOT ROMANTIC. Which is why there are so many celebrities who get restraining orders and there are anti-stalking laws.
I know there are lots more examples. These are only a few. Feel free to leave more in the comments. For now, I'm sick and tired and hungry so that's all I've got.