Showers? Only if your flying through a heavy rain storm and there is a hole in the ceiling!
Actually, I've never known any commercial planes to have showers. It is because water is VERY HEAVY and it would be way too expensive to supply that much water on a commercial jet.
So the answer is definitely NO. They do NOT have showers.
What you may be reading however, is that many airlines are building showers in the airport lounges for transit passengers.
They usually charge an extra fee for this GROUND service, even if you are a member of the airport clubs. Delta's is called the "Crown Room". I was told that if you pay the fee, sometimes as high as $50.00, that you can have this service even if you are not a members of that airline's club.