Since so little is known about Peter Quill's father, he could be anyone in the Marvel Universe. Guesses have ranged from Starhawk to Howard the Duck. However, there is one name I don't believe has been mentioned yet that seems like a very possible answer. Thane.
For those unfamiliar with the character, Thane is the son of Thanos and an unnamed Inhuman woman. He lived hidden from his father on Earth until undergoing Terrigenesis. His Inhuman abilities give him an unstable reality-altering left hand and a right hand that can trap others in amber in a state of "living death." His fear of his father and dangerous powers led him to flee Earth.
So how does Thane make sense as Star-Lord's father?
1) He's Half Inhuman
The Nova Corps stated that they found an anomaly in Star-Lord's nervous system that identified him as not entirely human. It allowed him to hold on to the Power Stone for longer than expected because he was more powerful than an ordinary human. It makes sense that Inhuman DNA was what gave him the extra power. If Thane is half Inhuman, that would make Peter Quill one-quarter Inhuman.
Note: Just because Peter has Inhuman DNA does NOT mean he has to undergo Terrigenesis. This could simply be avoided by saying he is not "Inhuman enough" for the process.
2) He's Half Human
A lot of people find it strange that characters like Superman and Lois Lane end up together because one's Kryptonian and the other is human. This is also an issue in the theory that someone like Starhawk is Star-Lord's dad. I mean, what would possess Meredith Quill to do the no-pants-dance with someone that looked like, well, Starhawk.
It makes sense that Meredith and Thane could conceive a child because he's half human. The biology of it lines up, and before Terrigenesis, Thane looked very much like a normal human being. It's more likely that they'd be attraced to each other.
Note: Star-Lord's father in the comics, J-Son of Spartax, also has a very human apperance.
3) He's Something Ancient
As Nova Prime explains to Peter that his father wasn't human, she mentions that he is something ancient that she hadn't encountered before. The Inhuman race has been around for millions of years, but their existence has been kept quiet. The Kree who created them abandoned them, and they've been hiding ever since. This could explain why Thane isn't in the Nova Corps textbooks.
4) He Left Earth
The reason Star-Lord's father abandoned his family is never specified in the movie, but Thane could have a few of reasons for leaving. The first is that he did not want to draw the attention of Thanos and put his loved ones' lives in danger. Thane could also leave Earth because of his Inhuman appearance and abilities. He didn't want his son to grow up thinking his father was some sort of monster. He also didn't want to risk harming his son with his unstable abilities.
5) He Sent Yondu to Retrieve Peter
For those who read the recent Black Vortex arc in the comics, you'll know that Thane relocated to the planet Brennan-7, where he became the protector and idol of a group of outcasts. His obligations there would prevent him from picking up Peter himself, so he would send Yondu and the Ravagers to bring him home.
6) It's All Connected
Marvel prides themselves on having a shared cinematic universe. Thane is a perfect character to connect several aspects of the MCU together. He's a character who could very easily pop up in Guardians of the Galaxy 2, Avengers: Infinity War, and Inhumans. Introducing him would be a great way to tie everything together. This would also make Thanos the grandfather of Star-Lord, which would make for a cool Darth Vader/Luke Skywalker moment. It's another way for Marvel to remind their fans of the big bad Mad Titan that lurks in the shadows.
Do I make any sense? Am I an idiot? Let me know in the comments! Who do you think is the father of Star-Lord?