Is supplemental insurance like critical-illness or accident coverage worth buying?

Usually no for people who already have solid major-medical coverage and an emergency fund. Critical-illness, accident, and hospital-indemnity policies pay a fixed cash amount if a specific event happens — a cancer diagnosis, a broken leg, a hospital stay. They're cheap and emotionally appealing, but they cover narrow, defined events and often pay less than you'd expect after exclusions. If you have a good health plan with a reasonable out-of-pocket maximum and a few months of savings, that combination already protects you against the costs these supplements target. The better uses of a marginal dollar are usually maxing your HSA, building your emergency fund, or buying adequate disability and term life coverage — the protections against truly catastrophic, lifestyle-ending losses. Supplemental policies make the most sense if your deductible is high and your cash cushion is thin, as a stopgap rather than a core protection.