"I wish you did"
"I wish it rained"
"I wish you were"
All of these statements talk about something that you wish to be/happen right now, in the present. These situations are unreal. E.g. I can't be taller, even if you wish it to be so.
As for your other examples (I wish you would . . .) - they essentially mean the same thing, but they generally contain a hint of criticism/annoyance. I wish you'd shut up.
I wish you'd stop.
(A tall girlfriend to her short lover): I wish you'd be taller than me
A: "I always put my clothes away."
B: "I wish you did" -> I wish that had been the case in the past.
A:"I always put my clothes away."
B: "I wish you would do." -> I don't accept what you say but I wish that, in future, you will put your clothes away."
A: "I live in the Atacama Desert and I wish it rained" -> ...and I wish that there were a normal rainfall pattern.
A: "The trees and the flowers are dying, I wish it would rain", -> I wish that there would be one occasion upon which it there is rain so as to water the plants.
"I wish you were taller" -> "I wish it were possible that you were taller, but I know it is not."
"I wish you would be taller"? [This is ridiculous: you are asking a person to comply with your wish and, somehow, grow taller.]