Just to get things straight, canon ships are romantic relationships that have actually received confirmation. If the characters being paired together are not a couple or they do not state they are in love with each other, the ship is not canon. That said, the only canon ships from Pokemon are minor character ships such as Norman x Caroline and Potter x Florinda. We know that the characters involved in those pairings love each other, so they are canon.
Pokemon does not have any canon ships involving Ash or any other main characters. If any main character ships were canon, a lot of kids would grow bored with the show because one of its main focuses would be romance. Granted, there are some kids who like romance, but the majority are not into it. If Pokemon was a show with any canon main character ships, most children would not want to watch it, since they would not like seeing mushy stuff on a regular basis.
When it comes to Pokemon, there are main character ships that are hinted at, but only for the sake of fanservice. The writers have no intention of making any of them canon.
If anyone wants to know what ships I like, they are:
Giovanni x Cassidy: Currently my favorite ship. Recently, I even wrote a fanfiction for it (I will not post it due to the fact that it is rather sexual) XD
They go great with one another. In Showdown at the Oak Corral!, Cassidy stated that since she was a little girl, she has dreamed of being a queen. I can see her taking a liking in Giovanni due to the fact that he is a wealthy and powerful man who could make her the queen she has always wanted to be. And Giovanni? The man is a player. There is no way he is going to pass up an attractive woman like Cassidy.
Jessie x James: If it were not for all of their unsuccessful attempts to capture Pikachu, Jessie and James could have become a couple. This is most evident in Training Daze. That episode truly shows how close and compatible they use to be. In the original series (Kanto, the Orange Islands, and Johto), a relationship between them still could have worked, since they were still close and their personalities continued to go well with one another. However, since AG, Jessie has been portrayed as being someone bordering on being insane and James has been shown as being terrified of her. I think Rocketshipping could still potentially work out if they stopped chasing after Pikachu and came out successful in another line of work. Success would do wonders for Jessie's mental health. If that were to occur, I am sure the spark that use to exist between Jessie and James would be re-ignited. I wish it would. I miss the Rocketshippy hints that use to exist in the show.
Giovanni x Delia: I find this ship interesting. If Giovanni and Delia had a relationship in the past, it was surely a turbulent one filled with angst. Being big on dark romances, I naturally love it.
Giovanni x Domino: It is clear that Domino is closer to Giovanni than just her rank would allow. Why else would she be allowed to talk back to him? And Giovanni? I cannot see him not going for Domino. He has a real eye for women.
Bashou x Buson: These two would make a good couple. Their personalities compliment one another and they share great chemistry.
Off-topic: I love those Steelshipping fanarts you posted, shedinjask. They are cute :)
Meowth x Butch: The only Pokemon x Human ship I support. They would make an awesome team. Together, they could help each other formulate intelligent schemes. I am certain that they would be really successful in carrying out crimes. Furthermore, their personalities are compatible with one another. Meowth is snippy and always wants to be on top while Butch is a relatively easy going and mellow guy. Overall, I think they would be happy together.