Four feet. That's in our current house. Our new build does not have an island, but it does have two openings between cabinets/counters and built-in appliances. We designed those to be four feet also.

In my opinion, three feet is not enough, especially if you have an opening appliance opposite the island. You need to be able to pass between the fully open appliance door and the island in safety and relative comfort. That takes four feet.

The minimum distance between the island and the cabinets is 42", when you have drawers or doors on cabinets.
You need 48" (or more) between the island and the refrigerator.
These are minimum dimensions, you do not want to have minimum if the island is "massive".
You do not want too much space in between because is not practical specially if you have to go back and forth between island and cabinets. These dimensions have to be adjusted depending on the specific case. Hopefully you involve a skillful architect or kitchen designer at some point.

If you care about "size creep" as I did, I have 40" around the island and open on one end. I wouldn't want the refrigerator size much further, it's very convenient transporting stuff to the island having it close.

At our old house, we had 32"-36" around our island (one side was open) and it worked just fine. If your appliance doors (oven and dishwasher) open towards the island, you just get used to standing to the side and don't think about it ever again. The refrigerator at our old house was just past the island so the door didn't open into the island, so I won't comment on whether it works to have the refrigerator door open to the island other than to say that I think it would work with the narrow doors of a side by side refrigerator but not with a full width door. I love islands and if the choice for me was between an island with 36" aisle or no island, I would go with the 36" aisle. At our new house we did 48" except in front of the cooktop where we wanted the island closer because it is convenient to be able to turn from the cooktop to the island without taking steps, but I never think that gee the wider aisles are so much nicer than the aisles at our old house. When you are calculating your aisle widths, be sure to take into account the counter overhang which will probably be 2" on the front of the perimeter cabinets and islands and 1" on the sides of the perimeter cabinets and islands--36" can turn into 32" if you don't.

I would stick to 42". The danger of a tighter space is that you might bend down to get something and bump your rump on the opposite cabinet and fall toward or drop something hot. Therefore the range oven door is the most serious limitation IMHO.

"I have read you want 3 feet on each side if the island, but that seems a little too close?"

Too close. I have 48" working aisles and my island seating/walking aisle is about 54" (it might be a little larger). How wide you need the aisles to be depends on whether they are purely working aisles or also walking. For example, lets say you have a U shaped kitchen with an island (kitchen is open on only one end, no door or other room on the other end). You could do a 42" aisle on the working side and then 48" on the seating side. But if that seating side is also a walking aisle (lets say there is a doorway from the garage or mudroom at the closed end of the U), you need a wider aisle because you need space behind seated people. Also, you need to consider if work spaces back up to each other. Let's say the prep sink is on the island and the range is opposite it. You need to have space for 2 people to work back to back. I would do a 48" aisle in that case. We did 48" wide aisles because we had the space and DH always seems to be underfoot. Our kitchen works well with multiple people in it.

With my dishwasher open I can fully open the drawers on the island opposite it without them bumping. Not sure I could do that with a 42" aisle. Now, some people will claim 48" is too much walking. I am 5'7", DH is 6'3". It is just a pivot. I don't feel there is too much walking. I do far more walking going back and forth to the pantry which is in the hallway between the dining room and kitchen.

So, assuming you have 24" cabinets on both sides of the kitchen, 48" aisles (maybe one is 42" and one is 54") and a 36" island you need need 15' for the kitchen. Mine is 15'6" or so.

Measurements given on plans are usually wall base cabinet to island base cabinet, so carolyn53562's point is well taken.

Open appliance doors vary in length and deserve individual consideration. For example, our open dishwasher door sticks out a hair over 26 inches beyond its base cabinet. Since we have 48 inches between the counter and the island, we still have enough room to pass between it and the open door. If we didn't it would be a royal pain putting dishes away.

We have a 42" wide (at widest point) island in a 13'1" wide kitchen. Work aisle is 36" where center of island is recessed 3" (used vanity for base) and tightest point is 13" from corner of end cabinet to open oven door, but since I tend to stand to the side when I open the oven that's not an issue. Walking behind the bar stools on the other side of the island is a pain though - I need to get smaller barstools with straight/no backs that can be pushed under the overhang when not in use. These huge angled Windsor backs do interfere with traffic (53" from edge of 13" overhang to basement door, and the barstool easily takes up 24" of that). DW is not an issue since it is in the corner and island isn't that long. Edge of counter is 32" from handle of French door fridge - plenty of room to pull out for servicing, but close enough to load and unload groceries.