Hi all.
Kind of new to Arduino and electronics in general, so this might seem like a noob question. Anyhow, I was wondering if it would be possible to use the Arduino board as a programmer, in the sense that I would burn my program to the ATmega controller, detach the controller, place it on another pcb and still have it working?
Welcome to the wonderful world of Arduino! 
Indeed this would work (I do this myself:)) you just need to make sure you have the minimal components. Here's a nifty link with a list of just what you need.
http://itp.nyu.edu/physcomp/Tutorials/ArduinoBreadboard
To program it with the board, connect the TX on the board to the TX of the chip, and the RX to RX, ground, and reset (if you want auto-reset when uploading).
Thank you
And thanks for the link! Very helpful!
Although this only shows how to program the ATmega on the breadboard. I was wondering if I could program the controller while still being on the Arduino and after that detaching the controller and using it elsewhere. Or is it the same principle?
Ah, yeah my bad.. that's what I was explaining after the link, it's the same principle. When I first put the chip on my breadboard, I connected the tx to rx and vice versa.. lol just wanted to point out, it's not that way. 
Ok, so if I program the ATmega on my Arduino board, then place it on, let's say a breadboard, what are the requirements for it to still function?
Sorry if I'm persistent, I'm just not following as much as I'd want to 
Ok, so if I program the ATmega on my Arduino board, then place it on, let's say a breadboard, what are the requirements for it to still function?
A power supply, a 16MHz crystal with required capacitors, and something to do.
I have just finished a project based on Arduino ATMEGA 328 processor - it uses 100nF blocking capacitors for Vcc and AVcc, 16 Mhz crystal and two 22pF capacitors. That's all for running a chip programmed before.