Bukhari, Muslim and Abu Daw'ud reported that 'Umar approached the Black Stone and kissed it.

Then he said:

"I know that you are a mere stone that can neither harm nor do any good. If I had not seen the Prophet (peace be upon him) kissing you, I would have never kissed you."

So basically, it's ONLY done because the prophet did it.

Bukhari, Muslim and Abu Daw'ud reported that 'Umar approached the Black Stone and kissed it.

Then he said:

"I know that you are a mere stone that can neither harm nor do any good. If I had not seen the Prophet (peace be upon him) kissing you, I would have never kissed you."

So basically, it's ONLY done because the Prophet did it.