Haruka in Haru Natsu Aki Fuyu, despite being ostensibly in a relationship with Akiho, keeps applying Skinship Grope on other girls, much to Akiho's anguish. Eventually, Akiho makes it abundantly clear that she doesn't like it, and Haruka stops. While not necessarily afraid of commitment, until then Haruka didn't see a need for it.
Michael in Macross Frontier, who is always hitting on girls but ignoring the not-subtle attentions of Klan Klan, his childhood friend. Eventually, he admits that he knows he has issues: since he's a soldier who could die in battle any given day, he's terrified of starting a real relationship with anyone, and therefore only dates girls he knows he won't get serious with. In the series, Klan manages to break him out of this by stating plainly her love for him, causing him to admit that he loves her too, but he dies shortly thereafter. In the movies, though, they both survive and wind up together.
Mary Jane Watson of Spider-Man fame had this vice because of the bad relationships both her parents and her sister and brother-in-law had. Peter proposed to her about three times before she said yes. And then...
Film — Animation
One of the plot threads of Despicable Me 2; Gru is shown several times having problems romantically relating to women, though at one point he goes on a date with a Paris HiltonExpy (a date which goes disastrously wrong, to his evident relief). At the end of the movie, he marries his colleague Lucy.
Film — Live Action
A central focus of the film Vicky Cristina Barcelona. The main characters cheat, lie, and even enter a polygamous relationship that's doomed to fail instead of finding and settling down with a single person in a healthy relationship. In the end the film is a Shoot The Shaggy Dog Story in that the main characters remain the same people and their experience in no way helps them with their issues in the future.
Uncle Buck has this in regards to his relationship with his girlfriend, the car repair business owing Chanice. It's just one of several ways he's presented as being unreliable at the beginning of the film.
Runaway Bride is about a woman with commitment issues that has almost been married three times, but has runaway from the wedding each time because of her fear (in addition to leaving a long list of boyfriends that never even made it to the engagement stage). Considering the film's genre it's not a spoiler to reveal by the end of film she finds someone to finally settle down with.
Shows up in Dave Barry's works, notably Dave Barry's Complete Guide To Guys, where men are afraid that they'll get in a relationship and get married and have kids and get old and one day they'll be walking down the beach and see a single guy relaxing in a hot tub with several supermodels and invite him and he won't be able to join them AAAIIIEEEEE!! He notes that to get the same amount of love and devotion with more reliability than a man, you might as well get a dog.
The Hunger Games: Katniss Everdeen spends the better part of three books fighting her growing feelings for Peeta Mellark because she doesn't want to get married and have children.
Penny has this problem in regards to her relationship with Leonard. The couple eventually works through it by Leonard putting the power to propose marriage in Penny's hands, so she won't have the weight of it on her shoulders until she decides she's ready.
Sheldon struggles with committing to Amy and then from there moving forward in their relationship. In his case, the issue stems from having previously thought of himself as a Celibate Eccentric Genius who is above time wasting romantic notions, and having an aversion to change. In one episode both Leonard and Amy decide to move too fast for their partners and put moving in on the table. Sheldon and Penny are forced to confide their hesitations about it to each other.
Howard goes through a sudden spell of commitment issues about committing to Bernadette. His problem is that he's too attached to some fantasy of actually being with some perfect-beauty actress like Megan Fox (and he has a slight illusion about distinguishing this fantasy from its chances of becoming reality, but not more than slightly.) A history of enduring the fate of the Casanova Wannabe can do that to a guy. He gets over it.
Torch Wood's Captain Jack Harkness has this, primarily of the afraid-of-outliving-love-interest variety.
Men Of A Certain Age has this as Terry's main problem to overcome. He's a middle aged man that still goes through multiple girls like he's a young twenty something.
Friends: It's one of Chandler Bing's defining traits. His parents had a messy divorce, and he's unable to trust, commit and be happy. He had struggles picking up women; when he succeeded, he broke things up over minor issues. He dated Janice who was nice enough, but a fairly insufferable woman who he stayed with because he thought he couldn't do better and that she was his only chance for a long-term relationship. (And she eventually chose another man over him). He also dated Kathy who he was crazy about but lied and cheated on him, making him even more scared of falling in love. He freaked out several times that he's destined to die alone. He later got together with one of his best friends Monica and they had a stable, loving relationship, but he still had several crises when he either got cold feet or thought that a minor argument means they are breaking up for good. Thankfully because they were so close before she faithfully reassures him about his fears, refuses to let him screw up and bolt, and they end up Happily Married.
Drake from Drake & Josh goes through a different Girl of the Week every episode (sometimes he'll go through multiple girls in the same episode). He's been shown to be afraid of being steady for too long and will often get bored with his current girlfriend very quickly (possibly the only exception is Carly, the record store worker, and even she disappears eventually). When his brother is struggling with The "I Love You" Stigma and asks him for advice, Drake's immediate response is that saying I love you is a trap.
Farscape: Chiana's Commitment Issues lead her to cheat on D'Argo with Jothee, D'Argo's son.
In Bell Book and Candle, after Shep and Gillian have been close for two weeks, he asks her when they are going to get married, and she recoils at the suggestion. They point out that they're reversing the usual male and female roles in this kind of argument. Her problem is that she would have to give up being a witch, but that's a secret she doesn't want to divulge to him yet.
Nathan in Guys and Dolls has been engaged to Adelaide for over a decade.
In Bye Bye Birdie, Rose nags Albert about when they will finally get married and settled down, after eight years. The two things holding Albert back are Conrad Birdie and his mother.
In the The Sims 3 this a trait you can give one of your Sims. Sims that have it will often get the wish to break up with whomever they're romantic with, and for other Sims to get a Relationship Upgrade with them the relationship meter must be particularly high. There is also a book entitled "Commitment Issues" Sims can read.
Similarly in Sims 2, a Romance sim will often fear marriages, committed relationships and having children
Rayne in Least I Could Do. At first he is presented as an unapologetic Jerk Ass womanizer, with little to no desire to ever be in a serious relationship. As the strip goes it delves into some Hidden Depths revealing his issues with commitment actually aren't as straight forward and shallow as they are initially presented.
It's implied Riff might have this hang up in Sluggy Freelance, although it could also be a combination of attracting crazies (even the ones he remains friends with) and not being the best at expressing himself.
Darius in Campus Safari, partially because he feels overworked by his position as headmaster of the Mars Academy and partially because both he and Sheana have a life expectancy of several hundred years so he figures they can wait. Sheana doesn't see it that way, especially when she's in heat.
Ginger Foutley in As Told by Ginger expresses this doubt in the finale. Ginger's mother is getting remarried, and Ginger's new boyfriend Orion is pressuring her to go steady, but Ginger doesn't want to because she doesn't feel comfortable. She wonders if this is wrong, but her friends suggest that she has commitment anxiety due to her parents being Amicably Divorced and because she once dated her best friend Darren. She and Darren had since broken up after he showed interest in Simone and felt guilty about two-timing Ginger. She also wonders how her mother could take getting remarried after being divorced once, but her mother reassures her that while nothing is certain, she's happy to remarry anyway.