The three jobs
Grip (no sliding, no folded corners), cushion (comfort and less fiber crushing), and protection (the pad takes the abrasion the floor would otherwise give the rug's back). Pads extend rug life materially and protect hard floors from rug-back coating transfer — three jobs, one unglamorous line item.
The type matches the floor
Hard floors: felt-plus-rubber (or natural rubber) pads — the felt gives cushion, the rubber gives grip. Carpet-over-carpet: thin Grip-it style pads. Rug-on-carpet: minimal or none (the carpet grips). Avoid PVC-heavy pads on urethane floors — some react chemically and stain; natural rubber and felt do not.
The trim-to-fit ritual
Pads trim 1 inch inside the rug edge (scissors, straight cut) — a pad showing beyond the rug is the visible mistake that outs the whole setup. Buy the size above yours and trim down; the $30–80 line item is the highest-return purchase in the rug category.