First of all, I have nothing against other people's beliefs when it is in the aspect of shipping. However, I also have the right to pinpoint reasons as to why their beliefs are incorrect (mine probably is, too, but I haven't noticed anything). With that over with...

Abuseshipping/Devastationshipping
In Giovanni's eyes, Mewtwo nothing more than a tool; a tool which would enable him to have power over the world. If he loved Mewtwo, he wouldn't have emotionally and psychologically abused him as he has done in the past. On Mewtwo Strikes Back, he lures Mewtwo into believing that someone has finally accepted the fact that he is more than a clone, only to betray him in the end by saying he was born for the purpose of being a slave to humanity. As for Mewtwo, he had complete trust in Giovanni, perhaps too much, yet who else did he have? No one. Maybe Mewtwo loved him for a time, and now despises him for the pain he caused.

Domainceshipping
Could Domino have an attraction for Mewtwo? Possibly, but I failed to notice any hints. As for Mewtwo, I doubt he thinks of Domino at all in a romantic or sexual way. Mewtwo's feelings toward people are harsh enough - he doesn't despise them, but he doesn't have faith in them, either. Having love for a Team Rocket member would be the last of people he'd ever love. He has a bad past with Team Rocket, and he loathed that Team Rocket returned to use the clones in vivisection, and him once more as a slave.

Mewshipping/Catshipping
This one is sweet, I'll admit ^_^; Personally, though, I doubt anything could spark between Mew and Mewtwo. They affilated at the end of Mewtwo Strikes Back, but on Mewtwo Returns, Mewtwo still carries the sullen fact that he is a clone. In my eyes, I believe that Mewtwo would try to edge from originals as far as possible, and have a clone for a mate instead. And...um... how would they breed? Mew's so ... tiny O.o

NewIslandshipping
Joy is beautiful, and Nurse Joys are well known, which would be appealing to trainers. Also, because of her medical knowledge, she was helpful for Mewtwo's research on creating clones. In other words, she was a practical tool for Mewtwo's counterattack. A possible relationship? I guess, but it'd only be one-sided, considering Joy was in a trance.

Psychoshipping
Ah, the popular Psychoshipping, often seen in fanfiction. The bonding is practical - Sabrina is the most powerful human psychic; Mewtwo is the most powerful Pokémon psychic (well, tied with Mew). Other than that, though, what other evidence is there? They don't even know each other! If they were to begin a relationship, they would at least have to know each other well enough. As of now, Sabrina doesn't even know of Mewtwo's existence, and the same goes for Mewtwo about Sabrina.

Others
Honestly, the only other character I can imagine Mewtwo falling in love with would be Ash. Ash, like Ai, is selfless. He treats Pokémon with the deepest of respect, and unconditonally saved Mewtwo's life. Mewtwo realized this. (But I still believe Mewtwo belongs with Ai :P)