you know about Team Rocket...
yeah, they are a Mafia... but considering the Events just prior to the beginning of Pokemon Blue/Green/Red and the events occuring in these games makes Team Rocket not THAT evil... they are trying to be the good guys! (like Team Magma in Saphir, and Team Aqua in Ruby)
"why do I think that?" - you ask? ... well let me explain:
befor the games start, Team Rocket is working on "Project Mewtwo" - to create the most powerful Pokemon in existence - so that it can do their bidding (and most likely serve as a bribing tool - "give us control or it'll decimate your city!") - Ok that is evil...
BUT
Mewtwo is self-aware, doesn't want to be controlled, gets an existencial-crisis and goes on a rampage - destroying the lab on Cinnabar Island and fleeing to the Cerulean cave.
NOW the game begins... and Team Rockets "evil plans" are involving capturing Mewtwo so it cannot run rampant and destroying everything!
They accepted that Mewtwo is uncontrollable for them, so they put every thing they have into stopping Mewtwo! ... well in their own "cruel" ways...
Encounters:
- The fossils at Mt.Moon - "Maybe the ancient Pokemon are strong enough to be able to keep Mewtwo at bay!" - The player denies that!
- Cerulean City - TM Dig - "We need to access that cave unnoticed... if someone sees a bunch of us someone might get suspicious!" - the Rocket Grunt at the nugget brigde is a lookout... to report if Mewtwo decides to leave the cave, and trying to recruit the player because he sees the potential in the player to maybe able to stop Mewtwo! - The player denies that!
- Pokemon Tower/Celadon City - Rocket HQ / Silph Scope - "There is an invulnerable Ghost Pokemon in the Pokemon Tower! - Maybe we can use it to stop Mewtwo!" Ghost-types are very effective against Psychic types... (the immunity to Ghost types in the first generation was sadly a coding error, which was not intentional!) - again the player denies that!
- Silph Co / Masterball - "This stupid brat is denying all of our plans to stop Mewtwo! ... If we can't battle it... we have to catch it! - I hear there is a prototype of a ball that can catch ANY Pokemon!" - They want to use the Masterball to catch Mewtwo as a final effort to save Kanto! - but yet again... the player defeats them... so Giovanni says: "Screw it! Take the Masterball kid! I hope you know that you have doomed us all!"
- Veridian Gym - Now Giovanni is just plain pissed! You foiled his plans and now you dare to stand before him in a gym-battle! - That man is already broken, now you are just giving him the finishing blow and he dismantles Team Rocket...
It is PURE LUCK that the plazer stumbles upon Mewtwo in the cave after becoming champion... you know, Mewtwo could have gone on a killing spree, while the player enjoyed being the champion! The player doesn't even have to go into that cave... it's totally optional!
Yeah... you just averted the destruction of the whole region and possibly more, by pure luck, and stopped an organization who would have done it, if you wouldn't have foiled their plan to do so... MULTIPLE TIMES!
The encounters on the Sevi-Islands in FireRed/LeafGreen are a different division of Team Rocket... they weren't in contact with the Boss or the rest... and so they didn't want to believe that Team Rocket was dismantled...
The Johto encounters, were purely to bring Giovanni back as their boss! They continued the research and experiments in hope that their Boss would return, to lead them again!
Team Rocket is the deepest of all of the other Teams... who are mostly just selfish, power-hungry fanatics...