- Commercial Airliners:
Both Concorde (service ceiling FL600) and the Tupolev Tu-144 (service ceiling FL660) could reach FL600. Most airliners have a service ceiling of around FL410 though.
- Business Jets:
According to this article the highest service ceiling for various business jets is at FL510, so none can reach FL600.
- Military Reconnaissance Aircraft:
The Lockheed SR-71 Blackbird had a service ceiling of FL850 and routinely operated above FL600. Many other aircraft in this category (e.g. MiG-25, Tsybin RSR, U-2, RB-57F, M-17 and M-55) can also fly above FL600.
- Military Fighter Jets:
Most fighter jets have a service ceiling below FL600, but there are a few that can fly higher (e.g. F-15 and F-22 with service ceilings of FL650, the MiG-25 again, and MiG-31 with the highest service ceiling of FL820+ for a fighter).
- Experimental Aircraft:
The rocket powered X15 reached space at 67 miles, nominally corresponding to FL3530.
The glider (!) Perlan II has a service ceiling of FL900 and actually reached 76,124 feet.
High altitude balloons and rockets can of course fly higher.
