Make my arduino project a stand-alone one.

For example if I want to create project of the most basic blinking led but I want it to work without arduino.I know that i can do it with an 555 timer IC.But it will only work for small projects.Some say that I can buy an atmega 168 or any such microcontroller and program it through arduino for the project needed.

InduinoX:
Some say that I can buy an atmega 168 or any such microcontroller and program it through arduino for the project needed.

They are correct, although for blinking a LED an ATtiny85 would be enough.

This page shows some of the common AVR chips:

All of them can be programmed as standalone chips with the Arduino IDE.

Do a search here and on google for 'standalone ATMega328' , 'Standalone Arduino' or 'Breadboard Arduino'.

Doing what you want is very easy. All you need is an ATMega328P-PU with Arduino Bootloader, a 16Mhz Crystal, 2 x 22pF Capacitors, a 10k resistor and a 5v supply. Add your LED and resisted and you have the hardware to run the Blink sketch.

There are plenthy of UK eBay sellers that do the components in kit form for a few pounds and deliver within two days.

If doing anything more then you'd want to add some 0.1uF decoupling capacitors at each pair of Vcc/Gnd pins.

In the long term it's much better to get a $10 ISP programmer then you don't need bootloaders, crystals, etc.

There is some advice at Prototyping small embedded projects with Arduino | David Crocker's Solutions blog. If you are going to do this a lot then I recommend you get a in-circuit programmer instead of using your Arduino as a programmer.