Question

How come Team Rocket are always after Ash's Pokemon?

Comments

asks about team rocket in question, uses Team Plasma tag

Answer 1

After Pikachu completely destroyed them in the first couple episodes, Team Rocket's view of Pikachu being a worthless Pokemon changed to one of 'this Pikachu is special'. Because of this Team Rocket just follows Ash around in order to try catch Pikachu and give it to their boss Giovanni.
Most of the time before they formulate some plan they start thinking of money, approval or PROMOTIONS :D

After their repeated failures they basically settled into getting any Pokemon - not neccesarily just strong ones. Well their end-goals are to get the strong ones, but they're fine with getting weak ones on the way. Also they kind of consider most of Ash's Pokemon at quite a high level :D

Answer 2

Well in the first few episodes, they think Pikachu is worthless and weak. But they find out that Ash's Pikachu is special and strong. They then make it their mission to capture Pikachu and impress the boss. But along the way, they'll pretty much take any Pokemon that they can get their hands on that they don't think is a weakling.

Source: I recently watched season 1. Hope I helped! :)