Around 400 miles for a normal runner.
The midsole of the shoe (the cushioning) will break down before the outer sole so even though the soles are not worn down, the support may be.
Your best option is to visit a shop, try on the same pair, if there is a noticeable difference then you know it's time for a change.
To make your shoes last longer, you should rotate two pairs, 24 hours rest will allow the midsole to regain it's shape.
I change my running shoes once a year or every 400 miles whichever is sooner.
The midsole will break down over time even if kept in the box and never worn.