Is an Anti Static Mat and strap neccessary when fixing computers to prevent static discharge?

[froggyboy604]

I think an Anti-Static strap is necessary when fixing computers, and a mat is necessary for laying a motherboard on top of the mat to prevent the motherboard from being fried by static electricity, but a lot of people ssay just touching the powersupply is good enough to ground yourself.

Some people even spray anti-static spray on a carpet to prevent static build up.

How do you check if the anti-static mat and strap are still functioning since the resistors wear out after awhile I heard?