City spacing is more a
gameplay style, like choosing your civ...
But, sometimes it depends on situation. Since ring-city placement (RCP) does not longer apply (as i understood from several posts) here's a general guideline:
For the cities to *ever* use the full 21 tile radius, they must be pop 20 or more, which means late industrial age (and possibly only one city earlier, with Shakespeares' Theatre). Many games are won by that time.
Cities like this are at distance of 4 tiles from each other (are as you said most of the time not colliding in radius).
Other people prefer the 3-tiles distance (city-tile-tile-tile-city) in an + pattern (north-east-west-south of current city). This way only 8 tiles of each city are shared). If laid in a X pattern (northwest, northeast, southeast, southwest), every city will lose possibly max 12 tiles.
Again, other people prefer 2-tiles distance (city-tile-tile-city). I think this is called ICS (infinite city sprawl). Every city has a max of 8 tiles to work with, the rest goes to specialists (if food allows it). The advantage of cities with 2-tiles distance is that a foot-soldier (movement 1) can move from 1 city to another in one turn via road.
(I used this alot in Alpha Centauri, but only with Hive and high-efficiency factions. I might even call the ICS: SMAC city placement

).
However, note that with growing number of cities the corruption grows rapidly (even in those cities that had minimal before). This is called "rank corruption" (each city has a number, as the number gets higher, corruption gets higher). Forbidden palace helps, police stations help, and corthouses help reducing the corruption (dunno which one though, distance or rank).
br,
-bibor aka kirby