Feel free to consider this a corollary to the power pop thread -- twee can be its sometimes more precious, sensitive friend.
I've been getting into twee pop lately, both the American and European varieties, some more recent but much of it "historical". If I had to make a broad, necessarily imprecise suggestion of differences between the two: American twee, exemplified by K Records, is usually more cutesy -- think: Beat Happening -- while European twee, exemplified by Sarah Records, is often at least as much depressing as it is hopeful -- like The Field Mice or most any Sarah bands. Both have generally fierce allegiances to a DIY ethos, lo-fi recording, and independent labels. The music, befitting its label is also often very melodic and the lyrics are your usual relationship-type stuff. Many of these bands, unsurprisingly, like The Beach Boys. Other influences are also not very surprising: Jesus & Mary Chain, The Smiths, The Velvet Underground, Daniel Johnston, R.E.M., etc.
More modern bands that take up the twee label vary, just as they did in the '80s or '90s. You've got your Camera Obscuras or Allo Darlin's with much more produced stuff but also your Tullycrafts, those fierce lo-fi heroes.
Okay, so what bands do I mean who are twee? Have some songs!
Beat Happening:
"Our Secret",
"In Between",
"Hot Chocolate Boy"The Cat's Miaow:
"Third Floor Fire Escape View",
"Hollow Inside",
"Don't Worry, This Isn't About You"Tullycraft:
"Pop Songs Your Boyfriend's Too Stupid To Know About",
"I Kept The Beach Boys"Dressy Bessy: "I Found Out", "Fuzzy"
The Softies: "Charms Around Your Wrist", "It's Love" "Snow Like This"
Heavenly: "I Fell In Love Last Night", "P.U.N.K. Girl"
The School: "Let It Slip", "All I Wanna Do", "You Make Me Hear Music (Inside My Head)"
Marine Girls: "Times We Used To Spend", "Second Sight"
Talulah Gosh: "My Best Friend", "Escalator Over The Hill", "Yalulah Gosh"
Television Personalities: "I Know Where Syd Barrett Lives", "This Angry Silence"
The Field Mice: "Emma's House", "I Can See Myself Alone Forever", "Canada", "This Love Is Not Wrong"
The Magnetic Fields: "Josephine", "100,000 Fireflies", "When You Were My Baby", "Lovers On The Moon"
The Pastels: "Up For A Bit", "Thru' Your Heart", "Sit On It Mother"
Camera Obscura: "Lloyd, I'm Ready To Be Heartbroken", "I Need All The Friends I Can Get"
Okay, I got lazy and stopped linking through that list. Look 'em up yerself!