What size wire for 150 A main electrical service
It depends on when the work was done, and which version of the code was being followed.  In the 2011 code and before, there was Table 310.15(B)(7). This table listed the service and feeder conductor size for 120/240 volts, 3-Wire, Single-Phase Dwelling Services.  The table listed 1/0 AL to be used for 125 ampere services. 

The 2014 version of the code omitted this table, because folks were simply using the values, and not applying correction and/or adjustment factors properly. The 2014 version allowed you to size the conductors to 83% of the service rating, which usually worked out to about the same as the old table.

Looking at your 150 ampere service as an example (Excluding any temperature or other adjustments).

150 ampere x 0.83 = 124.5  

Table 310.15(B)(16) says that 1 AWG copper is good for 130 amperes at 75C. So if no adjustments were needed, 1 AWG would be allowed as service conductors for a 120/240 volts, 3-Wire, single-phase dwelling service.