Historical dramas where the FL is a commoner?

Six Flying Dragons - Not only is FL a commoner, but I would say of her major role in the storytelling is to be a voice representing the common people. That being said, she's definitely not very carefree or stupid (she's lived a pretty rough life). Personally, I found her a bit bland (mostly because I don't enjoy Shin Se Kyung's performance very much), but the drama is GREAT! I should note that, while she is a major character, this show really has two male leads (they were important historical figures, FL is fictional).

Empress Ki - Technically, FL's father is a man of relatively high status, but she does not meet him until she is an adult (she grows up on her own as an orphan), so she never lived a privileged life. FL is definitely badass, but again she's not carefree or stupid (she's really smart).

Love in the Moonlight - I don't exactly remember FL's background, but I think she was a commoner. Also, I would describe her as carefree.

Warrior Baek Dong Soo - One of the FLs is noble, but the other is a commoner, who I think fits your description. Again, though, this is really a show with two male leads.

The Legend - It's been a long time since I watched this, so my memory might be a bit fuzzy. From what I recall of the female lead, I think you might like her.

FL is a commoner from birth who enters the palace or gets involved with nobles:

• +1 Love in the Moonlight - Although her father was involved in a political rebellion, both her parents were commoners. After being separated from her mother (who made her dress as a boy), the FL is raised by another commoner, then kidnapped and forced to become a eunuch (where she has to continue to pretend to be a boy). 
• Sound of the Desert - She was raised by wolves and later adopted by a noble Han scholar who served in the royal court of the desert tribes. She's a bit more quirky than "normal" or "stupid". She faces quite a few tough / sad situations, but her natural personality is pretty carefree. She definitely has her own strength. 
• Legend of Lu Zhen
• Hwarang - Not exactly a commoner. She's referred to as a "half-breed". Her father is noble but her mother was a servant.
• +1 Empress Ki - As noted above, she is badass, but definitely not "normal" or "carefree and a little stupid".

FL is a commoner in modern times who travels back to historical times:

• Splash Splash LOVE - She travels back in time as herself. 
• My Only Love Song - She travels back in time as herself.
• Ashi Girl - She travels back in time as herself. 
• The Eternal Love - Her soul travels to a different,  historical-setting world where she shares the body of a noble girl who was abused by her family and forced into an arranged marriage.
• The Eternal Love 2 - Her soul travels to a different,  historical-setting world where she takes over the body of a noble girl who was abused by her family and almost immediately becomes a servant.
• Moon Lovers: Scarlet Heart Ryeo - Her soul travels back in time and takes over the body of a noble girl. At one point she becomes a low ranking palace servant.
• Dreaming Back to the Qing Dynasty - Her soul travels back in time and takes over the body of a noble girl.

The FL is from a noble family but is raised in poverty / like a commoner:

• Sungkyunkwan Scandal - The FL's family is very poor. She has to pretend to be a boy in order to get work to support her family.
• The Tale of Nokdu - She is raised in a brothel.
• The King in Love - She was raised as the student of a martial arts master, or something to that effect.
• 100 Days My Prince

- Chef Hua  (FL is a chef for bodyguards) 

- Mi wo Tsukushi Ryouricho (FL is a chef) 

- Under the Power (FL is a constable) 

- Maiden Holmes (Fl is a detective)

- Damo (FL is a detective)

- Hwang Jin Yi (FL is a Gisaeng)

- The Painter of the Wind (FL is a painter) 

- Jewel in the Palace (FL is a palace maid) 

- Thong Ake Mor Yah Tah Chaloang (FL is a pharmacist) 

- Maids (FL is a maid) 

- Tempest (FL is a Eunuch)