Question about the Microcontrollers

I'm pretty new to electronics development, I got a parallax homework board and it's pretty fun, but the problem is the stamp is built onto it and parallax is really expensive stuff. So I'm thinking about getting an arduino and using some ATmega8 controllers. I just wanted to know, after you program the controller can you put it directly onto a breadboard with all the circuits going correctly and such and power will it still operate as if it were stocketed onto the arduino?