Stumpy and Pretty utterly despise each other and have what is possibly the worst relationship on the show. The two of them are almost always fighting, verbally or physically.
Stumpy started hating Pretty the moment he first met her, in "Let's Play Truth or Dare". He insults her almost all the time, and even hits her sometimes. However, he has flirted wih her on occasion. In "Let's Play Beach Volleyball", he tries to flirt with her, even before he accidentally drinks her love potion. In "Let's Play Clone Party", he flirts with her while disguised as Mr. Cat, which she finds to be charming before finding out who it really is. She tries to hit him, but decides not to because she is unable to bring herself to punch anything that looks like Mr. Cat, so she calls her sister to do it for her. In "Let's Play Top Models", he joins his friends in an attempt to publicly humiliate her after she makes fun of them.
Pretty hates Stumpy and considers him to be ugly, stupid and annoying. She often insults him and beats him up for even the most minor annoyances, or gets her sister to hit him instead. In "Let's Play Curse of the Pharaoh", she (along with Kaeloo and Quack Quack) neglected to save him from drowning in quicksand until he pointed out that their supplies were in the backpack he was wearing at the time. Later in the episode, they both repeatedly hit each other, and they end up fighting for the magic yogurt. At one point in the episode, Stumpy thinks that there are rattlesnakes on the ground, so he he jumps into her arms. She gets angry at him, throws him on the floor and wipes her feet on him like a mat. In the episode "Let's Play I Like You", Pretty posts humiliating pictures of Stumpy (and the others) on Fakebook. Stumpy later retaliates by taking an absolutely humiliating photo of her and posting it himself.
The song "Heads and Tails" shows their relationship in a more detailed fashion. Interestingly, the video shows that while they aren't friends, they may not completely hate each other, and can get along.
In Season 3, Stumpy is implied to have formed a crush on Pretty, despite already dating Ursula. In "Let's Play Afterlife", he tried to spy on her when she was about to take a bath, but Kaeloo stopped him. In "Let's Play Telepathic Gladiators", his imaginary version of Pretty kisses him on the cheek. The feeling may or may not be reciprocated, as in "Let's Play the School of Lies", Pretty kissed him on the lips offscreen as a reward for saving her from some aliens.