My three year old has officially entered the why phase and I am losing my mind. Every single sentence I say is met with a why. Even when I give a long answer, he just says why again. How do you all stay patient without just saying because I said so every five minutes?
##The Endless Loop Solution##
TechNavigator, welcome to the club! My daughter used to do this until I was ready to hide in the closet. I found that they often do not even care about the answer, they just want to keep the conversation going because they love the attention.
###Try the Mirror Trick###
When they ask why for the tenth time, just look at them and say: That is a great question, why do YOU think? Most of the time they will stop and think for a second and then come up with some wild story about magic or space. It turns the pressure off you and puts the work on them.
###Make it a Game###
Sometimes I just give the most ridiculous answer possible. If he asks why the sky is blue, I say because a giant blue octopus painted it last night. Usually, that gets a laugh and breaks the cycle.
if you try to be a walking encyclopedia you will burn out by noon. I started telling my son that I only have five answers left for the day. Once I use them up, we have to wait until tomorrow for more whys. It sounds mean but it actually makes him think about which questions are actually important to him!
I noticed my kids use why as a way to stall for time. Why do I have to put on shoes? Why is it bedtime? Why do we have to eat broccoli? In these cases, it is not curiosity, it is just a delay tactic.
I give one solid explanation and then I stop. If they ask why again, I just say: I already told you the reason, what did I say? If they can repeat it back to me, then they know the answer and the game is over.
Last week we were at the store and my son asked why we couldnt buy a toy. I explained once. He asked why five more times. I just started asking him why back until he got annoyed and stopped. It was a small victory but I felt great.
GorillaBlink has the right idea with the why do you think response. My kid usually says I do not know, you tell me! which is when I just say I am not sure either, let us go look it up later. That usually ends the immediate interrogation because kids have the attention span of a squirrel.
My favorite move is to just start singing. Why are we going to grandmas? Because she has cookies and we love her so much! If you make the answer a song, they get confused and usually forget what they were even asking about. Works like a charm and keeps the mood light. 
##The Deep Dive Method##
Sometimes they actually are curious and I try to respect that. If I have the energy, I go into a super long, boring technical explanation. I will talk about light waves and atmosphere and refraction until their eyes glaze over.
###Bore Them to Silence###
If you give them way too much info, they eventually realize that asking why leads to a twenty minute lecture. They start being a lot more selective with their questions after a few rounds of that.
###Why it Works###
It shows you are willing to talk but it also makes the interaction a bit of a chore for them. It is a win win because they still learn something but they stop the rapid fire questioning that drives parents crazy.
@WovenLap, the five answers a day thing is hilarious! I am definitely trying that tomorrow. I usually just pretend I did not hear the third why and start talking about what we are going to have for lunch. Redirection is the best friend of any tired parent.
I think we forget that they are just trying to learn how to be people. It is annoying for us but for them, everything is brand new. I try to be patient but yeah, after the 50th why before breakfast, even a saint would start to snap. Just keep some coffee nearby and remember it is just a phase.
If you really want to mess with them, answer their why with another question that makes no sense. Why is the grass green? Because the cows are busy! They will look at you like you are crazy and usually just walk away to play with their Lego.