One of many of Carl Jung's archetypes, the Hero, is a vital part of the plot of the Pokémon anime, as it focuses on heroes and heroic acts to keep the plot going. Ash Ketchum of Pallet Town started as the original hero, and at the time of this writing May has been included as one as well. However, they may or may not fulfill the same qualities of a hero, but we shall determine their heroism as the essay progresses.
Wikipedia notes that a hero "usually fulfills the definitions of what is considered good and noble in the originating culture. Some scholars place the willingness to sacrifice the self for the greater good as the most important defining characteristic of a hero." Indeed, both Ash and May represent goodness and nobility. They are only rarely unwilling to help others (Misty seemed to be the most compassionate, replaced by Max, who is now the one team member who helps out even the most arrogant, selfish and misunderstood character), doing everything from running simple errands to saving threatened individuals, human and Pokémon alike. A willingness to self-sacrifice, however, rests mostly on Ash's shoulders. May just has not been required to give her life for anything, the eighth movie notwithstanding (she was absorbed not by her own choice). Ash, on the other hand, has risked his life at least twice. First in the first movie to stop the catastrophic fight between Mewtwo and Mew, and second in the eighth movie, where he understands that his aura will help Mew save the world and willingly transfers that energy to Mew until the process is dramatically interrupted.
One point made on the Web site is that heroes were not always positive, at least with regards to other people or environments. The heroes of ancient Greece could just as well defeat random monsters as destroy the landscape, injure or kill innocent people or non-humans, bring about disease and financial ruin, etc. Again, May does not fit this aspect with nearly the exactness that Ash has. Ash has created a lot of the situations he has to fix by the end of the episodes. He is almost always guilty of trespassing or stealing (events of which he is of course unaware, but the fact is that he never asks if someone might own the property he just uses). When he takes his friends to a carnival, it is only Max's presence that awakens Jirachi, which thereby permits the villainous Butler to siphon its energy to recreate a monster. If she had not been so smitted with Ash, Latias probably would not have stuck around Altomare in plain sight for so long, which allowed thieves to learn of her whereabouts. Whenever Team Rocket's Jessie, James and Meowth are in trouble, Ash must be persuaded to help them by the most compassionate member of his team. True, they do wish to steal his Pokémon, but their chronic ineffectiveness in this regard should humanize them more to Ash than it does.
Searching Wikipedia for "women + hero" is rather upsetting. Many describe sports athletes or the random feminist, of which May can not really be classified authoritatively either way. May is a Pokémon Coordinator, a person who in this world might attend dog shows and the like. Except for learning some basic strategies and theatrical poses, she doesn't have to train her body as much as her Pokémon do. Nor is she a feminist hero, since that would probably be more attributable to Misty than her, who struck out on her own to run her gym after her sisters left for more personal pursuits. If friendship is a trait of heroes, May definitely qualifies, sticking with Ash through thick and thin, but not once in my memory can I describe a scene like in the second movie, where Misty dives into chaotic waters to rescue an exhausted Ash from drowning.
It may be that May just simply was left out of the hero business by the writers, who apparently never really enjoyed the independent Misty anyway. Although she could be considered a co-star, she never really had to face heroic situations with the same frequency or intensity as Ash has, making her, fair or otherwise, less of a hero than Ash Ketchum.