We are finishing our basement and I'm wondering if it is worth putting in insulation if there is only a 3 degrees temperature difference from my upper floors to my basement. This is during the winter months. The temperature in my basement stands at 66 degrees in the winter.
A couple things to consider. If you have heat ducts in the floor of the upper level (i.e., the basement ceiling), you may be losing heat into the basement; insulating them (and especially sealing any leaks) may prevent heat from being "wasted" by warming the basement. Depending on the floor surface above, insulation may make them a bit more comfortable (although I would not expect a dramatic difference with the basement that close to room temperature), and may provide some sound insulation if that matters.
If you don't have warm-air ducts in the ceiling, and sound isn't an issue, the payback on saved heating costs would probably be pretty long.
If there is currently no insulation, the basement is being heated from above. Putting in insulation would thus make the basement somewhat colder, and reduce the heating-costs upstairs. How much depends on how well the basement is insulated from outside.
Insulation also helps with soundproofing, if this matters to you or now, depends on what you use the basement for, so can only be answered by you.
If air moves freely between basement and house (i.e. no plastic-membrane or other air-tight barrier) then insulating it may make the basement moister. What happens is that warm are (which can carry more moisture) gets into the basement where it's colder, which leads to higher moisture (or in extreme cases even condensation - you've surely seen that warm air with moisture that hits a cold surface sometimes causes condensation) If this is a concern, it might be an argument against insulation.
For me, a 66F (18C) space is a bit cold. I am okay with that temperature at night while sleeping, but not while I'm working in my office or just sitting watching TV. Retrofitting for insulation after the basement is finished is a major task, and basically involves tearing down all the exterior drywall and hoping you've done the studs correctly. Depending on your finish, it's at least half the work it would take if the basement was totally unfinished to start with, and more work if you have bathrooms or tile work or lots of interior walls touching.
Consider not just your use, but future use. If I was purchasing the house from you, my offer price would not only reflect my thinking that the basement is effectively unfinished (because I have to redo it), but that I also have to spend a day tearing out and disposing of half the work you've done.
The other aspect to this is that your basement is currently being heated, so of course there is not a huge temperature difference. You are likely losing a large amount of heat through the walls. The change you'll see when you insulate is that your furnace will run much less often and your utility bills will be lower as a result. One way you can see this is by using an infrared thermometer. Compare the temperature of your basement walls to your upstairs walls. I would suspect your upstairs walls will be very close to room temperature, and your basement walls will be more in the 10C / 50F range.
To me, this is a no-brainer. Insulate the walls and put in a vapour barrier (or use closed-cell spray foam, which is WAY better insulation and doubles as vapour barrier, but is more expensive). You should also consider insulating the floor or putting in a raised sub-floor. I did this in my basement and it feels basically the same as an upstairs floor (both in the temperature, and the "feel" of walking on it) instead of cold, hard concrete with carpet on top.