What aircraft fly faster than 250 knots indicated airspeed under 10,000 feet for safety reasons?
A 747 taking off at or near max gross weight will have a flaps up, minimum safe airspeed and climbout airspeed speed greater than 250 knots. In such cases you didn't notify ATC as they expected it.

I tried to find what the exact numbers would be at 840,000 lbs, but I seem to have thrown out that manual. I did, however, find a reference for a 747-200 with JT9D-7Q engines that gives the flaps up holding speed at 800,000 lbs as 259 kts at 5,000 feet.

Also, I do remember being on an arrival once, with the weight low enough that we could safely maintain well below 250, but that when we saw we were icing badly, we speeded up to somewhere around 300 to get the ram air temp above freezing. In that case we notified ATC that we were doing so.

Also, ATC occasionally requests max speed. For example, on Hajj flights into and out of Jakarta Halim airport in the late 1990s it was common practice for controllers to put you down low to get you under the traffic into Cengkareng airport. They would then often request max speed.