Why does the water in my toilet bowl look likes its moving around in the bowl? I had a leaking flapper and replaced it so to test it I turned off the water to the tank to see if it leaks down. It does not but the water in the bowl is gently waving back and forth.

Your sewer pipe should vent through the roof. Try and note if this happens when it is windy. Strong winds blowing across your vent might be causing the water to ripple a little. To make certain your new flapper is seating properly, and not leaking, place some toilet bowl cleaner or food coloring (some sort of indicator dye) in the tank and see if the water in the bowl changes color. Obviously a leaking flapper will cause the water in the bowl to ripple too.

I agree with scott. Let us know if its windy outside when this is happening. Even with perfect plumbing drainage and vent, on windy days, the toilet may show signs of "movement in the bowl". As long as you aren't getting extreme "waves", you should be good to go.

"gently waving back and forth. " like side to side or what. How high is the water level in the tank compared to the top of the overflow tube?