Each insurance company has different standards. I was an Insurance Broker before I became a SAHM. Most are around the 25 or 30 year mark. I would check specifically with your insurer.
If it is already in your home that you are currently insuring I wouldn't bother inquiring about it. They will contact you when they want an inspection done.
If it is in a new home that you are purchasing the insurer will most likely want an inspection done, the age of tank, pics of the tank etc...
Some people don't like the hassle that they have when there home has an oil tank or a wood stove. I personally don't either and wouldn't even consider buying a home that has either, unless it was a great price and I could afford to switch to gas. But that is just my opinion, and I am sure many people will differ from me.