Not really - there's a condition called CIPA (Congenital Insensitivity to Pain with Anhidrosis) ...which the person can't feel pain. In most cases it also means you can't feel your bladder is full, or that you've cut yourself, or have an infection, or broken bone etc. They also have a lot of trouble regulating body temp and can die from fever or hypothermia etc.
It sounds like not having pain might be nice, in theory, but in practice it's often a death sentence due to related complications.
