i will go with either

if you don't, don't - by jimmy eat world *its very stripped down*

or

Gone So Young - Amber Pacific -> sad but awesome

if a guy played Hold by Saves the Day for me I would be obliged to marry him then and there

i played "Every Thug Needs a Lady" by the Alkaline Trio for a girl once. she dug.

All Time Low - Remembering Sunday

Although it's slighty upsetting.

I've never in my life played a song to a girl, but I enjoy playing

Hey Jonny Park (Foo Fighters)
Play Crack The Sky (Brand New)
Atlantic City (Bruce Springsteen)
Upward Over The Mountain (Iron and Wine)

When I have a strum on the acoustic.

Poker Face

Thrice - The Weight
Thrice - A Song For Milly Michaelson
As Tall As Lions - Love, Love, Love (Love, Love)
Death Cab For Cutie - I will Follow You Into The Dark
The Decemberists - The Hazards of Love 2 (Wager All)
Bon Iver - Blood Bank

play crack the sky will always be a favorite.

ive only ever personally played my own song forecast the overcast one-on-one to one girl though, and thats the girl i wrote it for.

I played "Feeling This" by Blink for a girl once, and "Love Like Rockets" by Angels & Airwaves.

Both went down well :)

Kill The Music by ETID.

my exgirlfriend was pretty stupid, she heard me playing New American Classic and thought it was for her, should have read the lyrics really haha.

One girlfriend I cared about I'd just play her favourite songs, like There Is by Boxcar Racer and If It Means Alot To You

oh god, too many.

Just Like Heaven - The Cure
New American Classic - Taking Back Sunday
Hear You Me - Jimmy Eat World
Sam, As In Samantha - Tiger Lou
Play Crack The Sky - Brand New
First Day Of My Life - Bright Eyes

That's just the ones I can think of off the top of my head. I used to do practice acoustic runs by playing those songs to whoever I was with. Oh and I've played a lot of originals as well.

I Want To Save You - Soco
Remember to Breathe - Dashboard
I Want To Know Your Plans - Say Anything

At Last- Etta James
Gin War- Cassino

Sidenote- If you learn to play 'At Last', and can sing it well, it will work EVERY time.

Gender is a social construct. I play my the same stuff on my bass around/for my girlfriends that I do my guyfriends.