Why does the wicket-keeper wear pads in cricket? Is it a rule, or is it a choice they make?
No, the wicket-keeper is not required to wear pads. To quote from Law 40.1:
The wicket-keeper is the only fielder permitted to wear gloves and external leg guards.
(my emphasis) Note that's "permitted" not "required". As for why, that's simple - being hit on the shins by a cricket ball hurts.