You may want to check out:

• (500) Days Of Summer
• Silver Linings Playbook
• Romancing The Stone
• The Ugly Truth
• It's A Boy Girl Thing
• Little Manhattan
• The Perks Of Being A Wallflower - maybe
• Leap Year (2010)
• Jeux d'enfants (2003) a.k.a. Love Me If You Dare
• L'arnacoeur (2010) a.k.a. Heartbreaker
• One Fine Day (1996)
• Rapa Nui (1994)
• Witness (1985)
• Far And Away (1992)
• Two Lovers (2008)
• Japanese Story (2003) - maybe; it's relatively slow, but it does fit your other criteria.
• As Good As It Gets
• De rouille et d'os (2012) a.k.a. Rust And Bone - strongly recommended
• Sur mes lèvres (2001) a.k.a. Read My Lips - maybe
  Two bonus titles, in case you'd ever get in the mood for a
  slow, poetic
  romance movie:
• In The Mood For Love
• 3-Iron

Roman Holiday
Bonnie And Clyde

This is an unusual one: Wishman
http://www.imdb.com/board/10103273/?ref_=nv_sr_1

Here are a few I enjoy, that meet some or all of your criteria:
The Lover (though more of an erotic drama than a romance per se)
When Harry Met Sally
You've Got Mail
The Thomas Crowne Affair
Moonrise Kingdom
Sense and Sensibility
The New World (though, if you don't enjoy slow movies, this will not be your cup of tea)
Formerly Nothin_but_the_Rain

The Thomas Crown Affair
(both versions)
Educating Rita
The Stunt Man
When Brendan Met Trudy

• quirky romance between a straight laced school teacher and a free spirited small time crook, served up by Roddy Doyle
  Not sure either of the two main characters are likable, but the story is believable and the acting is top notch throughout:
  Venus (2006)

The best romance ever made is Roman Holiday.
The best modern example (relatively modern) might be When Harry Met Sally
Based on your criteria, you might also like:
Sabrina - the Humphrey Bogart one
Annie Hall
The African Queen
Cold Comfort Farm
Roxanne
The Sure Thing
Leap of Faith
The instrument has yet to be invented that can measure my indifference to that remark.

I would rather see something like, two people who wouldn't typically get along falling in love.
Much Ado About Nothing (2012)
Les combattants (2014)
(Love At First Fight)
mf
I know that, in spite of the poets, youth is not the happiest season"