The basics
Store watches in a fabric- or leather-lined watch box with individual cushioned slots. The box keeps them organised, dust-free, and prevents case-on-case scratching. Stack-style winders are unnecessary unless you have perpetual calendars (see above). Position the watch dial-up if possible; this rests the balance pivot in its preferred position and minimises rate drift over storage.
What to avoid
Magnetic exposure: phones, laptops (especially the speaker/hinge area), MagSafe chargers, magnetic clasps on bags, and surprisingly, magnetic-base toothbrushes. A magnetised watch will run +30-300 sec/day until demagnetised; demagnetising tools (CHF 30-50) fix this in seconds. Modern silicon and Nivachron hairsprings are magnet-resistant; older watches with steel hairsprings are vulnerable.
Humidity: above 60% RH, gaskets degrade faster and the case can develop internal condensation. Avoid bathrooms (post-shower humidity spikes), unconditioned basements/attics, tropical climates without dehumidification. A small silica-gel desiccant in the watch box helps. UV light: dial colours fade with sustained UV exposure (especially red, orange, lume); keep watches out of direct sunlight.
For long-term storage
If you're storing a watch for 6+ months without wearing it: fully wind it once, set the time, and let it run down naturally. The full wind pushes lubricant into all bearings before the watch stops. Don't continuously wind it; just one full wind. Re-wind and re-set every 2-3 months to prevent oil pooling. Annual gasket inspection if water-exposure is in the watch's near future. After 5+ years of storage without service, get a service before resuming wear.