After some years of experience with PIC microcontroller and PicKit2 I'm considering the purchase of Arduino Uno.
The problem is I don't want to buy an Arduino Uno Board for every single project I'm going to make because that would be expensive. Is it possible to buy only one Arduino Uno Board and then buy lots of ATMega328 microcontrollers (which cost just about 2-3 € each) so when I need one of them for a project I just attach it to the Arduino Uno Board, program it, then detach it and use it in whatever electronic circuit I need?
If that is possible, do you think would be better to buy ATMega328 with bootloader for Arduino already installed (like this one: ATMega328 with Arduino Bootloader)
or to buy regular ATMega328 which are cheaper and then install the bootloader myself? Is there maybe some Arduino Shield for installing Arduino bootloader on regular ATMega328?
If you do go ahead and purchase the Uno, you can then use that to program the 328 by using it as an ISP Programmer. Have a look at the following link for more information.
Building an Arduino on a Breadboard
If you don't plan to change the "sketch"/program that is loaded onto the 328s frequently you can even bypass using the Arduino bootloader, this also has the advantage of freeing a small amount of space.
I agree with @SantinoPrice here.
Using the Uno as an ISP is a fantastic method, and does exactly what you require.
I have used this in several of my own projects, programming a variety of ATTiny and ATMega chips.
Thanks a lot for your replys! 
I also read the article you linked and I think I'm going to go for the Arduino Uno Board, which is a simpler and quicker solution even if a bit more expensive.
I need to ask just a last question in order to make sure I undestand well: can I program every regular ATMega328 microcontroller with Arduino Uno Board, even the ones that don't have the Arduino Bootloader already installed?
Tricka90:
I need to ask just a last question in order to make sure I undestand well: can I program every regular ATMega328 microcontroller with Arduino Uno Board, even the ones that don't have the Arduino Bootloader already installed?
Yes, you can. You can program any ATmega. ATmega without the bootloader requires programming via ICSP. Arduino UNO can does this job easily with Arduino as ISP. With this, you can burn the bootloader and plug it into the UNO board for next programming or just to program it directly without the boootloader feature if it is not needed.
Get ATmega328P not ATmega328 for standalone. Or, Pro Mini boards have crystal and regulator built-in and are extremely inexpensive and are often used for leaving in a project.