Hoshi no Koe
Haruka na Machi e - Doesn't have much romance. Just a crush. Highly recommend this story though the girl and her ambition are not the main point.
Bakuman - Girl wants to become a voice actress.

Ashita no Ousama - wants to become a playwright
Gokinjo Monogatari - wants to become a fashion designer
Saiunkoku Monogatari - wants to become prime minister

Avatar by tassyn.livejournal.com

Reading: Kingdom, Sangokushi, Historie

Uwasa no Midori-kun!! - I don't like it, too smutty, but the girl wants to beat her childhood friend in soccer (he tricked her into having sex for a bet when they met years later)
Honey Hunt - girl wants to be an actress to beat her mom (I don't think anyone is scanlating right now)
Beauty Pop - girl wants to be a beautician/hairstylist. Cute.
Sugar Princess - girl wants to ice skate (on hiatus) by same author as Hana Kimi (Hana Kimi is AWESOME)
Kitchen Princess - girl wants to cook
The One - model
Charming Junkie - model
Venus Capriccio - ambition doesn't show up until later, mostly it's the guy who ends up wanting to succeed - piano. Very sweet manga.
Kiniro no Corda aka La Corda D'oro. Didn't like it much, but a lot of people love it - wants to become violinist (doesn't realize she actually wants to until a little while in though)