Short term disability insurance is good, but in my experience, long term disability insurance is worthless and a bit of a scam.
My wife has Lupus and had a hard time of it for over a year and was unable to work after a medical procedure didn't go so well. Well, her short term disability kicked in for a few months with no problems, then when it was evident that she may be off work for a longer period than we first realized, long term came and took over. For both short and long they send a pile of forms every month for both you and a doctor to fill out. No big deal, but when long term kicked in, the first letter we get was telling us that we were to apply for Social Security disability or they they would cut her benefits by the end of the first month that LTD was to kick in. So we had to trudge through the bureaucracy of that mountain of paper work and eventually did get approved for SSD and my wife was dropped anyway from her long term disability insurance since there is a clause that they won't pay if SSD is being collected.
So basically, for over five years that my wife paid into having long term disability, as soon as she needed it, they threatened to cut off all benefits if we didn't apply for SSD during the first month of coverage and dropped her anyway after SSD was approved. They just rake in premiums and pass the buck to tax payers when they should be covering it.