Some basic city patterns;
Optimal City Placement (OCP): You don't waste any tiles. Cities are at least 5 tiles apart (CxxxxC). You need hospitals to get the full benefit of the 21 tiles, but when you do, you have no overlap and powerful cities.
Loose Build: You have a small amount of overlap in your cities, but they can still get to size 12 and beyond. You don't need hospitals, but they don't hurt - even without them, you'll have an ok amount of cities with good production. Usually CxxxC.
Tight Build: Usually the tightest you can get before ICS. This is used in Always War (AW) games and games on higher levels where you won't fit in as many cities, or if you plan to have lots of wars. Units can go from one city to the next with roads in one turn, so it is useful for defending. It's CxxC.
Infinite City Sprawl (ICS): Cities spaced 2 tiles apart. Rarely get above size 6, but you get a lot of unit support. CxCxC. High corruption too, though, since you have many cities and reach the optimal city number soon.
I personally prefer OCP/loose build for my games, depending on the difficulty. Almost all of my games last until the later game, so I can get a good amount of production, yet still be prepared for the middle ages.