Why do Jessie and James want Ash's Pikachu so much?

Question

In almost every episode of the Pokemon anime, Team Rocket members Jessie, James, and their Meowth ("To protect the world from devastation...") try to steal Pokemon from our heroes, typically Ash's Pikachu and sometimes other Pokemon that happen to be being featured in that episode, though there is quite a bit of fixation on Pikachu specifically. For example, in The Joy of Water Pokemon, Jesse exlaims "Who cares about Chansey, let's get that Pikachu!", to which James responds, "Roger".

Why do Jesse and James and company care so much about Ash's Pikachu?

• Do they consider Ash's Pikachu an especially perfect example of a Pokemon?
• Is Pikachu an especially rare species of Pokemon, such that any example of one is very valuable?
• Is there a bounty on his head?
• Is it intended as revenge against Ash?
• Is it simply coincidental, as the show tends to omit Team Rocket's heist attempts except the ones where Ash's Pikachu is in danger?

Answer 1

In Episode 3 ("Ash Catches a Pokémon"), Team Rocket says the following:

Jessie: The only Pikachu we want is that one.

James: We're only looking for the rarest, most valuable Pokémon in the world, kid.

Jessie: And that special Pikachu is just the kind of Pokémon we need.

Presumably, this is the same reasoning they care for the remainder of the series. There is probably a pride element as well: Pikachu has foiled their plans so many times that if they could finally get back at them, it would all be worth it.