WMG: Evita

Narrator/everyman that appeals to Eva's conscience to help the poor like she promised? Works with the people, particularly during A New Argentina? Makes sense that he'd have a vested interest in the country if he IS the country. Also, who better to narrate a story about Argentina's most famous citizen than the country himself?

At least in the film version, Che is a projection of part of Eva's personality
This explains why he's always around Eva, having apparently followed her from her hometown to Buenos Aires. It also explains why she doesn't notice that her neighbor, some guy from her hometown, the barkeep, and roughly half the waiters all look the same.
  • It's worth mentioning that in the first half of "Oh What A Circus," the melody matches up with "Don't Cry For Me, Argentina" almost perfectly.
    • It doesn't just match up with it, it *is* it, just faster and in E rather than D-flat.

Che is a Time Lord
He got stranded on Earth and decided to amuse himself by following the life of one Earthling who caught his interest. The reason she never realised that he was following her is because he was using a low level perception filter to stop people from noticing. The real clincher however is the waltz for Eva and Che, for it was established in 'The Girl in the Fireplace' that Time Lords can interact with people inside their heads. He mentions that he might "seek worthier pastures, and thereby restore self-esteem", aka, he's grown tired of following her.

As an anti-Peronist Marxist, he's going to want to make Eva look bad.

Che is many people, not one
Admittedly more of a Doylist WMG than a Watsonian one, but at least in the film a number of Che's guises seem to be mutually exclusive with each other - he's both the poor laborer who inspires Eva to set up her charity fund and a guest at the swanky party Peron brings her to in the "Peron's Latest Flame" sequence, for instance. The easiest explanation would be that in reality (well, fictional reality), all these characters are different people stepping into the narrator's role when required, and are played by the same actor for convenience's sake.
  • This was originally canon, believe it or not. On the original concept album, "Che" is really a Brechtian "everyman" type of narrator (even masquerading as a "research chemist" more than once, including singing lyrics about insecticide (!) Only when the stage version was being put together did the director (the famous Hal Prince, who later directed the London "Phantom" as well) specify that he should be identifiable as Che Guevara (never mind the historical inaccuracy of that idea. In fact, "che" can mean "[a] guy/dude/etc." in Spanish (see The Other Wiki for details on that one,) so...yeah.

Che loved Eva
Assuming he's not Guevara (and he's not played as such is some productions), and he's not multiple people, this may be the most likely explanation for what his deal is and why he keeps following her. He portrays her negatively in his narration because he's jealous and thinks she belongs with him. In the film Banderas's portrayal gives off a "jilted boyfriend" feel at several points, particularly the fact that he basically spits "Don't look down; it's a long long way to fall" at her as he watches her dance with Peron at the inaugural ball. At the very end of the film, he and Peron also share a rather Worthy Opponent-esque stare, and he practically makes out with Eva's coffin.