Yes you can ask to change seats on an airplane and if there are empty seats on the airplane available the airline will usually allow you to switch seats as long as you are switching seats in the same class of the airplane.
I was on an airplane once and there was this very annoying kid who was kicking my back seat and I tried to be very nice about it.
He continued to do so and threw a temperature tantrum and he was around 8 years old.
I finally asked the flight attendant if it were possible for me to move to the back of the plane where there were a couple empty seats.
She was very nice and told me that I could do so and all I had to do was ask.
So yes you can usually change a seat on an airplane if there are seats available or if someone wants to switch seats with you.