While I plant very crowded, I think the best rule of thumb is to give the tomato plants plenty of room to allow for aeration. That should help prevent the onset of fungus problems and possibly the movement of fungus from plant to plant.
The only reasons I plant close and crowded are because I know I can in my normally hot, dry climate and I believe the practice increases production for a given space. I believe that tomato plants have a genetic propensity to either produce a lot of fruit or just a few fruit according to the variety. Since I plant Better Boys which seem to want to produce lots of fruit, I think I get triple the fruit in the same space by planting triple the plants. If the plants have sufficient food and water, they don't seem to mind being close to each other.
I tried the same thing last summer with Bell peppers. It was a total failure. I planted a few groups of plants with three plants in each group with the root balls touching. I also planted single plants properly spaced away from the other plants. They all received plenty of water and food. The single plants grew nearly four feet tall and produced large peppers all summer. The grouped plants started off well and had a lot of small peppers which would not grow larger than golf balls. The grouped plants only grew to about two feet tall. When the mid summer heat arrived, the grouped plants died. The single plants survived the heat and started blooming and producing again when the late summer weather cooled.
I just like to try different things, but what I learn is only applicable in my climate and my soil and water conditions.