One good example would apply it to a default static route on a stub router - A router that has only one way of forwarding all traffic outwards to - As such this route and its defined next hop should really never change so you could make it a permanent route
Paul gives a good example of a scenario where it would be appropriate to use the permanent parameter on a static route. Another scenario might be where you were running BGP and had a network that you want to advertise in BGP. Part of the requirement for advertising a route in BGP is that the precise same route (same address, same mask) must appear in the IP routing table. Many of us might use a static route to null 0 for that route. But it would also be appropriate to configure a static route with the permanent parameter which would guarantee that the route was always present in the routing table.