The short answer
3 days
Reykjavík plus one day trip. Tight, doable, more of a sample than a trip. Best if Iceland is part of a longer Europe route.
5 days, the sweet spot
Reykjavík, the Golden Circle, the South Coast (to Vík or Jökulsárlón), and one buffer day for weather. This is what most first time visitors should book.
7 days
Add Snæfellsnes (Iceland in miniature) or slow the South Coast down. Better than rushing the Ring Road in the same week.
10 days
Ring Road with breathing room, or the East Fjords, or a slow trip with hot springs and quiet towns. This is when the country starts slowing down around you.
14 days
The full Ring Road plus the Westfjords, or a Ring Road with proper rest days, or one base and deep slow travel. Two weeks is when Iceland stops feeling like sightseeing and starts feeling like staying.