Sorry, baby. I love you. I mean it. 
Yeah, I’ve been thinking this would be a fairly short thread if it were about love songs in which both parties seemed health and stable.
I’ll always love you and make you happy,
If you will only say the same.
But if you leave me and love another,
You’ll regret it all some day:
You told me once, dear, you really loved me
And no one else could come between.
But now you’ve left me and love another;
You have shattered all of my dreams:
In all my dreams, dear, you seem to leave me
When I awake my poor heart pains.
So when you come back and make me happy
I’ll forgive you dear, I’ll take all the blame.
This always struck me as vaguely creepy and stalkerish.
‘Common People’ by Pulp. I don’t think that flame will burn long.
That classic stalking song Every Move You Make was once commonly played at weddings.
‘With or Without You’ by U2. ‘nothing to win, and nothing left to lose’ =/
First couple of songs I thought of were Pink’s “Don’t Leave Me” and Florence Welch’s “Kiss With a Fist”. It sucks just a little bit that I love, love love the second one, cause when people really hear the lyrics they’re all 'WTF?!!" But I just really love the beat and don’t take it too literally.
I am not sure this is just what the OP means, however, cause I’m not sure either song’s focus is giving off any impression that they really think it’s a healthy relationship. 
"I broke your jaw once before
I spilled your blood upon the floor
You broke my leg in return
So sit back and watch the bed burn
Love sticks
Sweat drips
Break the lock if it don’t fit
A kick to the teeth is good for some
A kiss with a fist is better then none"
Pink’s Don’t Leave Me
"How did I become so obnoxious?
What is it with you that makes me act like this?
I’ve never been this nasty
Da da da, da da
Can’t you tell that this is all just a contest?
The one that wins will be the one that hits the hardest
But baby I don’t mean it
I mean it, I promise
Da da da, da da"
The Pink song came out right when my then-roommate’s 16-yr old daughter was in a pretty stormy relationship with her boyfriend, and I thought it fit her perfectly. They used to literally throw furniture at each other, though I am pretty sure it was mostly the girl who started and did it; he’d try to leave and she’d chase him down the road and try to make him fight. It was…pretty fucking disconcerting, actually. Hope she got some help, cause it was the definition of unhealthy for her to be so obnoxiously violent for no real reason.
How are we supposed to know for sure?
I came in to mention Kiss With a Fist, Every Breath You Take, Nightvision Binoculars, and If I Were Invisible. The first two were already mentioned, the third failed the ‘deliberately stalker’ criterion, and so perhaps only the last one counts.
What I refer to as the “Wanderer/Runaround Sue Paradox” says a lot about some very outmoded views on what are acceptable relationship behaviors for men and women.
“The Wanderer” and “Runaround Sue” are both songs by Dion and the Belmonts. The first one features a guy (quite proudly) declaring that he’s the type “that likes to roam around” and hook up with multiple girls, some of whom know that he’s not the monogomous type.
The second song is the same singer warning other guys about this girl, Sue, who broke his heart because she dates a lot of people…which is what Dion said he was doing in “The Wanderer”.
So obviously, Dion thinks that it’s cool for him to date lots of girls, “happy as a clown”, but if Sue dates lots of guys, she’s a filthy whore and guys should “keep away” from her. Yeah.
Heh, I misread that as “Pink Floyds Babe, Don’t Leave me Now”. Which has unhealthy ideas about love, but it’s not exactly meant to be a subtle love song 
Actually, come to think of it, it might actually be meant as somewhat of a love song by the speaker, as he is screaming out in an (admittedly unhealthy) cry for attention, understanding, and love. Only we are meant to understand that it isn’t really a love song.
Love the song, love the singer, and I know that she’s purposefully going over the top… but all of her songs about love are a bit cracked, and I don’t doubt that there’s a seed of truth in this one. In both good and bad ways, she’s the type of girl I usually end up with.
She meets a guy who doesn’t call her back, describes their entire non-existent relationship (down to having named their children), and describes how much she wants to kill the woman that the guy is dating instead.
"i would have waited like a week or two
but you never tried to reach me
no, you never called me back
you were dating that bleach-blonde girl
if i find her, i swear, i swear…
i’ll kill her, i’ll kill her
she stole my future, she broke my dream
i’ll kill her, i’ll kill her
she stole my future when she took you away"
There’s the Beatles’ “Run for Your Life”
I’d rather see you dead little girl,
than to be with another man.
You better keep your head, little girl
If I see you with another man
You better run for your life if you can, little girl
Hide your head in the sand, little girl
If I see you with another man.
That’s the end, little girl.
The first line was actually taken from an Elvis song, but John Lennon still ended up hating the song and saying he wished he’d never written it.
Jonathan Coulton’s "Skullcrusher Mountain"
It’s about a woman whose high standards won’t allow her to see beyond her suitor’s choice of career. Sad.
That’s immediately the first song that popped to my mind. I try to avoid listening to lyrics too closely for most songs, but that one has so little going for it musically, that you’re pretty much stuck with the lyrics. This is one fucked-up relationship.
It’s actually just called “If You Wanna Be Happy.” And it was the second song I thought of at this thread title, but I read it as a bit more tongue-in-cheek. You missed my favorite (spoken) line: “Say man. Hey Barry(?). Saw your wife the other day. Yeah? Yeah, she’s ugly. Yeah, she’s ugly but she sure can cook.” It’s so over-the-top I can’t help but crack up every time I hear it.
ETA: I did not know this, but apparently the song is based on this old (1934 song) from Roaring Lion. ETA2: Here’s another version by Roaring Lion, which I like a bit better.
Not that the song is mistaken by many, but I recall a girl in high school who thought she was giving me and my girlfriend (my wife of going on 20 years) a compliment by saying that Landslide by Fleetwood Mac should be our song. I recall double- and triple-checking with her as to her meaning, because I was a little offended, but she just thought it was a lovely love song.
Dolt.
How about “Love the One You’re With”. A song that says that if you’re travelling away from your SO, you should have an affair with whoever is conveniently around you.
Is that what that song’s about? I always thought it had a “there’s plenty of fish in the sea” type message about not pining away for someone who didn’t return your interest, but I admit I’ve never paid much attention to the lyrics.
"I accept and I collect upon my body
The memories of your devotion
I feel your fists
And I know it’s out of love
And I feel the whip
And I know it’s out of love"
- Antony & The Johnsons, ‘Fistful Of Love’
"Mr. Muscle forcing, bursting
Stingy thingy into little me, me, me
But just “ripple” said the cripple
As my jaw dropped to the ground
Smile smile
It’s true I always wanted love to be
Hurtful
And it’s true I always wanted love to be
Filled with pain
And bruises
Yes, so Cripple-Pig was happy
Screamed “I just compeletely love you!”
And there’s no rhyme or reason
I’m changing like the seasons
Watch! I’ll even cut off my finger
It will grow back like a Starfish!"
- Antony & The Johnsons, ‘Cripple & The Starfish’
The whole song fits into this category but I know I can’t post the entire lyrics so I’ll link them instead.
Yeah, IMHO it would be easier, and quicker, to list the songs with healthy ideas about love!
CMC fnord!
But, Bill makes it clear in the other lines,
… I said brother if you only knew you’d wish that you were in my shoes …
… I wanna spread the news that if it feels this good getting used, … just keep on using me until you use me up …
… It ain’t too bad the way you’re using me 'cause I sure am using you to do the things you do …
He doesn’t really care about how she treats him, 'cause he’s only with her for the sex.
“Don’t stick your dick in the crazy . . . unless you know you’re sticking your dick in the crazy!”