I like:
Rocketshipping (Jessie x James): My favorite pairing ever. I have always thought Jessie and James looked good together, but I did not begin to really like them together until the St. Anne arc, which had some nice Rocketshipping moments in it. My love for the pairing only grew from there as more hints for it were dropped throughout the series. The end of "Holy Matrimony!" made it my Pokemon OTP. However, at that point, I still was not that obsessed with Rocketshipping; I just favored it over all other Pokemon pairings.
"Training Daze" is what made me a fanatical Rocketshipper. That special shows how much depth and meaning Jessie and James' relationship has. It also shows the void they filled in each other's lives. James is someone Jessie can actually trust and rely on. Unlike the other partners assigned to her in Team Rocket, he is dependable and always willing to please her. He is also so sweet that she feels comfortable enough to occasionally show her softer side to him. Meanwhile, Jessie is someone James can work for and who provides him with the support he needs in life.
Furthermore, their personalities are opposites in a way that they are compatible with one another. Jessie's short-tempered, brash, and dominant while James is gentle, sensitive, passive, and rational (well, he is more so than Jessie XD). They balance out with one another perfectly.
Also, who does not like a relationship in which the female is dominant and the male is submissive? As a dominant female myself, I like to see that in shows (probably why I am also very fond of Amber x Wilson from House M.D.).
Diamondshipping (Giovanni x Delia): Diamondshipping is only canon in Pokemon Live!, but the concept is interesting. If Giovanni and Delia had a relationship in the past, it was surely a turbulent one filled with angst and drama. As someone who loves dark romances, I am fond of it.
Carnivalshipping (Butler x Diane): In addition to having a good backstory, Butler and Diane's love and dedication to one another is touching. Their romance is part of the reason as to why Jirachi: Wishmaker is my favorite Pokemon movie.
Roseshipping (James x Kate): As a Rocketshipper, I should hate this pairing, but I cannot help but like it. Kate is a nice girl, and seeing James act brave and heroic for her was adorable. I guess you could say I like this as a side pairing (Rocketshipping being my main pairing).
I do not like Pokeshipping. Ash and Misty would make a terrible couple. They are both hot-tempered and stubborn characters who always want to have things done their own ways, hence the reason as to why they constantly argue with one another. Their personalities clash badly. If they were to become romantically involved, they would have a great power struggle between them.
Furthermore, Ash is not interested in Misty romantically. Sure, Misty does have a crush on Ash, but what concrete evidence is there of Ash having romantic feelings for Misty? He has gotten embarrassed over people accusing him of liking her. However, that does not prove he has romantic feelings for her. After all, there are other fictional characters who have grown embarrassed over being accused of having romantic feelings for characters they are not the least bit interested in.
Examples:
1. Akane blushed in the Romeo and Juliet episode from the second season of the Ranma 1/2 anime when Ranma accussed her of wanting to be kissed by Kuno. Of course, every Ranma 1/2 fan knows that Akane finds Kuno repulsive and would not touch him with a ten foot pole.
2. When a Celestian calls Reid Meredy's prince in Tales of Eternia, he blushes. However, he does not have romantic feelings for Meredy. The game's writers were clearly intending Farah x Reid and Keele x Meredy, not Reid x Meredy.
3. In Tales of Legendia, Senel blushes when one of the characters (I think it was Norma) accuses him of being romantically involved with Shirley. He also gets embarrassed whenever he is accused of liking Chloe. However, he is in love with Shirley's older sister Stella, not Chloe or Shirley. Senel views Shirley as a platonic younger sister while he views Chloe as a good friend and partner on the battle field.
So you see, embarrassment is not the equivalent of romantic attraction.
Pokeshippers often claim that Ash was jealous of Danny and Rudy. However, I fail to see how he was.
Ash was not mad over the fact that Misty had a crush on Danny. Initially, he did not care that she was attracted to him. However, when Misty insulted Ash for not being as mature as Danny and chose to cheer for Danny instead of him, that was when he got angry. It was not because he was jealous of Danny. It was because Misty, who had been his friend for over a year, had not only insulted him, but had chosen to side with a guy she had just met instead of him. If I had just climbed a mountain and my good friend chose to share his or her blanket with someone he or she just met instead of me, I would ask, "But what about me?", too. Really, it was more like Ash felt mad not only over Misty's insult, but also that she chose to side with a stranger instead of him.
As for Rudy, Ash was angry over the fact that he was ignoring him, not that he was flirtatious with Misty.
Now, "The Ghost of Maiden's Peak." The end shows Ash being stunned by Misty's elegant appearance. However, one must keep in mind that Misty looked completely different at that moment than she normally does. Usually, she is tomboyish in appearance. I will admit that Ash probably did feel some sort of attraction to her in that scene, but that is only one time. When she dresses as she normally does, he views her as being another one of the gang. So, for Ash to feel any sort of physical attraction to Misty, she would have to dress girly all the time. Given Misty's personality, I cannot see that happening.
Contestshipping annoys me. My main beef with it is that it is a love-hate relationship in which the guy frequently insults the girl in order to get her attention. This makes the girl feel angry and upset. However, she is still attracted to the guy despite the fact that he is a jerk to her. Overall, I find those types of pairings disgusting and hate to see them done in fictional works. Those got old when Star Wars was new (though at least Han and Leia's relationship became tolerable in Return of the Jedi).
I dislike Neoshipping. The only reason people ship Butch and Cassidy together is because they are partners within Team Rocket. However, they do not have any chemistry between them. Hell, they do not even appear to be friends. Cassidy cannot even get Butch's name right XD
I also dislike Eldershipping, Palletshipping, Yamushipping, Kokoshipping, and Harley with any female character. Eldershipping is too fluffy and boring for my tastes. Palletshipping, Yamushipping, and Kokoshipping are rival pairings that are often twisted by slash and fem-slash fans as having romantic tension when they really do not. The characters in those pairings except for Ash and Gary really do dislike each other. However, with Ash and Gary, they grew to become friends, not fall in love with one another. As for Harley x Any female, he is homosexual, so that is impossible.