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).
Wikipedia has a list of altitude records, often by experimental craft. The 60,000 feet limit was surpassed around the end of the second world war with the advent of rocket and turbojet engines. Two notable achievements:
The rocket powered X-15 reached space twice. In 1963 it climbed to 67 miles, nominally corresponding to FL3530. Note that the X-15 did not self-start.
The glider (!) Perlan II has a service ceiling of FL900 and actually reached 76,124 feet. It utilizes standing waves forming at mountain ranges which under certain conditions can extend into the stratosphere. From wikipedia: "A sailplane at 90,000 feet altitude flies in approximately the same aerodynamic regime [...] to be experienced by a moderate size aircraft flying near the surface of Mars."
High altitude balloons and rockets can of course fly higher.
Depending upon the definition of Service Ceiling the English Electric Lightning just squeaks into the military fighter list. For early variants, if the climb profile was carefully managed, it could operate for about 90 seconds at FL600 before the airspeed bled off to the stall point.