I love a romance where the unattractive girl or girl with "unconventional looks" gets the guy.  I was also looking for dramas or movies with a plus size heroine but those seem hard to come by unless it is a story where the girl loses weight or undergoes extreme plastic surgery and I want to stay away from that.  So if you know of any dramas or movies with an unattractive heroine, or a heroine who is usually overlooked for being painfully shy, quirky, or awkward gets the guy in the end (basically I want to root for the underdog) please recommend them to me!  Thanks!

This is kind of a tough one. Most of the time the "unattractive" female leads aren't ugly, but there are a few that may fit what you are looking for.There is Fated To Love You Taiwan and Korean, which involves a nerdy/unattractive woman who accidently gets pregnant from a handsome/rich guy. The male lead's character is in a long term relationship with a pretty ballerina. Also  High School King of Savvy which also has an age-gap between the main leads.My Name Is Kim Sam Soon is older, but it is still really good. 
Here is a few dramas/movies that might suit what you are looking for ^ ^

Crazy Little Thing Called Love - (Thai movie) Unattractive girl is in love with Mr. Popular at school.

Busu to Yajuu - (Japanese drama) This has not been subbed that I know of. Sorry >.< However it can be still found without subs on drama sites (e.g. Dramanice). The story is quite easy to follow, short episodes & the heroine girl is plus size.

High School Debut - (Japanese movie) Heroine is a tomboy that is never had a boyfriend or tried to be girly before. A popular and handsome boy in school helps her to find a boyfriend.

Moon River - (Taiwanese drama) Heroine is a martial artist tomboy, starting at a new elite school from the country. When she arrives, she gets into a fight with the most popular arrogant and pretty boys in school. She then needs to apologise to their leader. The story progresses from there.

I hope that I have helped, and that you enjoy!!



Something that kinda fits what you want is the Taiwanese version of Hana Kimi. Out of all of the versions she is the one who looks the most like a boy, and yet the male lead still falls in love with her. And if you're willing to go down the more tomboy route Coffee Prince is the classic example of tomboy gets the guy.

Kimi Ni Todoke- It's a Japanese movie not a drama, but the lead girl scares everyone in her class because they think she looks like the girl from the movie The Ring, and the most popular guy in class falls for her.

Woody Sambo- She doesn't have a real different look to her, but she does have trouble getting a boyfriend because she's crazy strong, smells like BBQ meat, and she's flat chested (they harp on that quite a bit in the drama). The main guy and her go from becoming friends to falling in love. These are the only drama's I can think of that weren't mentioned already, that don't have some makeover element to them where they try to change the girl's outward appearance.
She Was Pretty

Coffee Prince 
Zhong Wu Yan
Ugly Duckling Series: Perfect Match
Cubic she's not ugly but for some reason the guy thinks she's not good looking.
I Want To Become A Hard Persimmon Same concept^
Wow! Thanks for all your suggestions!

tashe_12-My Name is Kim Sam Soon has to be one of my favorite dramas ever; I have also seen Fated to Love You and it is really good and fits in with what I am looking for.  I have not seen High School King of Savvy and it looks like it fits in with what I am looking for as well.

Daniella_Bella-I haven't seen any of the dramas/movies you listed!  Thanks for the recs; they seem to be exactly what I am looking for.

squeakyelle-I have watched Kimi Ni Todoke and I really enjoyed it. I will try the other two you mentioned---thanks for thinking of some recommendations that don't feature a makeover:)

CherryBunny-I recently watched She Was Pretty and really loved it. Coffee Prince is another good one that I have watched and enjoyed.

Lettuce_patchQueen-I have seen Cubic and you are right the heroine in that is not ugly at all--she is gorgeous!  I have seen Ugly Duckling: Perfect Match and it definitely fits in with the types of dramas I am looking for.  I have not heard of the other two you mentioned and I will give them a try---thanks!
masters sun 
heart to heart
my pig lady
Full house take 2 .... she's obviously a pretty girl IRL but not that attractive in the story
Now I would like to see a drama where the guy lead is just average looking... Not sure I know of any, lol
Nobuta wo Produce (jdrama) and Yamato Nadeshiko Shichi Henge (jdrama) both have a heroine who is considered not to be pretty and non-sociable and gets help from good looking male leads to become prettier & more sociable. Both actresses are pertty though.

First thing I actually thought of though was Scent of a Woman (kdrama), it's not plot-wise stated that the main female lead is ugly or anything. But she's definitely (and obviously) older and less pretty than the other girl that's also in love with the main male lead. 

Since it's been longer since I've watched that one, I'm not too sure about it, but Mary Stayed Out All Night (kdrama) might fit your description too. It's not stated that she's ugly either, but I would say she's average/common girl (and a drama lover at that <3) and the female concurrence is definitely better looking in my opinion. 
The Taiwanese drama "The Rose".