How can i have the same effect of a camera flash with little LEDs?
For example in the olympic games we can see all the camera's flashing.
I want to achieve the same effect with LEDs

Lumileds makes LED that are suitable:  http://www.lumileds.com/
Linear Tech, Maxim, Zetex, and others make driver chips:
www.linear.com
www.maxim-ic.com
http://www.zetex.com/

Here's one design note:
http://www.linear.com/pc/downloadDocument.do?navId=H0,C1,C1003,C1042,C1031,C1061,P7810,D5580

I don't know if you could recreate the same kind of flahes you'd get
at the olymic-type events.

The reason that those show up like that are because flash lamps in
cameras use extremely high intensity bulbs that require capacitors to
charge large amounts of energy. Not only that, but sometimes you see a
"star" around the flash, (kind of like when you're driving down road
at night) that's because of imperfections in the TV camera len's, if
you were at the olympics and didn't have glasses on it would just look
like hundreds of little points of light.