"The boy is turning the table around and around."
"The boy is turning the table round and round."
As others have said:
the boy is turning the table around
You would probably think that he is turning it just one full rotation or less.
"around" is not needed and putting it just once suggests 180 or 360 degrees.
the boy is spinning the table around
"spinning" suggests many rotations, but also some speed or freedom of motion. Again, "around" is not needed or could suggest one full or half turn.
"Spinning around and around" would be saying the same thing twice.