Boiler will not shut off (by 3 users)

Boilers are controlled by a few things, one being a thermostat, secondly a zone valve or circulator control and thirdly by an Aquastat that controls the boiler temperature and safety shutoff. If one of those controls is sticking, your boiler will turn or remain on until it reached a temperature where the safety control shuts it off. If your boiler is not shutting off at all, most likely it is the Aquastat control. The Aquastat will be located on the boiler and may have "Honeywell" printed or stamped on it. Take off the front cover and you will find model numbers on the backside of the cover. If you have some mechanical skills, you could probably replace it. Turn off your power first and wire it wire per wire.
If your boiler is shutting off on high limit, I would suspect a stuck zone valve or circulator control or a bad thermostat or shorted thermostat wire.