How much more does it cost to fab a 4 layer board compared to a 2 layer board and is it worth it?
Some reasons to move to 4+ layer:


Need additional routing space
Need power and ground supply planes due to current draw
Need to control trace impedance.  You can only control the impedance of a trace if it has a consistent reference on the adjacent layer(s).  This is critical for signal integrity of many signals but mostly associated with medium-high speed digital and/or long traces.
Need low noise performance, either analog or digital.  Its almost impossible to pull this off without at least a ground plane in the stack up.
EMI: Unless you're able to devote the bottom to a full ground pour you have to be very vigilant with your ground return paths to avoid current loops.


I'm sure there are more, that's just what popped into my head.

I've personally never had a board fabbed that wasn't at least 4 layers so I can't say too much about the cost of 2 layer.  

The move to 6 or 8 layers is usually what I have to fight with and most of the time the same rules I listed above are the driving forces, with the addition of needing to route very high speed signals between plane layers to reduce EMI.