Should You Refrigerate Butter?
Salted butter doesn't need the fridge. In a covered dish, in a cool spot, it stays fresh and spreadable for a week or two. Keep out only what you'll use in that time, and refrigerate unsalted butter.
Why butter is fine on the counter
Butter is mostly fat, with very little water for bacteria to grow in, and the salt in salted butter is a natural preservative. Kept covered, away from light and heat, it simply stays soft and ready to spread. That's the whole appeal: butter that actually spreads, without tearing your toast.
How to keep it out
Use a covered butter dish or a French butter crock, out of direct sun and away from the heat of the stove. Leave out about a week's worth and keep the rest in the fridge. If it ever smells sharp or tastes a little off, that's rancidity from air and light, toss it and start fresh.
When to reach for the fridge
Chill your butter if it's unsalted (no preservative), if your kitchen runs warm (much above 70°F), or if it's simply more than you'll get through in a week or two. Everything else can live happily on the counter.
I keep mine out on the counter in a covered dish, so it's always soft and ready. And I only buy French butter, the higher butterfat and cultured flavor are worth every penny. Once you've had it, there's no going back.