depends on which definition of PIC you want to use.
PIC is short for picture, and it can be short for the microcontroller that a number of users here use, the PIC16F84 (I think).
A microcontroller is 1/2 a computer. The thing you need to supply is the code, input, and output.
The input can be switches, or buttons, or previous outputs.
The output can be a LED, or a LCD.
The code is what is first injected into the microcontroller before it functions. The code "controls" almost every aspect of the microcontroller.
What do you mean by powerful?
Go to 8052.com, and you will see all microcontrollers that work with the 8051 instruction set.
I am using the at89c2051. It has 2K of flash memory (code space), 128 bytes of ram. Even though it is little space, I benefit from the size (for the 8051 compatible controllers). It is only 20 pin DIP chip.