There are multiple reasons (and theories. People won't give up with Pokémon theories & creepy pasta) of why Team Rocket would like to get Ash's Pikachu.
1) The most realistic answer (in my opinion) is that the Team Rocket Leader asked them to. But why would he want THIS Pikachu?
In the Season one episode "Ash Catches a Pokémon," when Team Rocket was trying to steal Pikachu, Meowth accidentally says that Ash's Pikachu's power exceeds the power level he would possess as a Raichu (the evolved version of Pikachu).
As said in the wiki, as an example. (I'll try to update the post with a video link).
Which can be interpreted as
Ash's Pikachu has got more power than a regular Raichu
As you can see in the different seasons of Pokémon, Ash's Pikachu is dunking asses. If you compare it to a regular Pikachu from one of the games, the difference in stats is ridiculous. I mean like... really?
What's more, Pikachu is one of the few Pokémon Ash didn't abandon (I mean.. C'mon, he left Charizard, who in the world would be insane enough to do this? What do you mean, Pokémon have feelings too?), so Ash spent many years training him.
So we can assume that, even if Ash was one of the most incompetent trainer, Pikachu should be around level 100, giving the Team Rocket another good reason to try to catch him.
2) Another way to see it (not proven at all, just my personal opinion) is that, more than being stupid, Team Rocket is incredibly stubborn, as proven by the hundreds of tries of catching Pikachu. They spent years trying to catch Pikachu, what would be the sense of all this time of their lives if they stopped now? They prefer to keep spending their time trying to catch this Pikachu rather than admitting they lost years of their lives for nothing.
TL;DR : Pikachu OP & Team Rocket stupid