Contrary to likely misunderstanding, stars usually do not collide during galaxial collision, because the stars only constitute a very small portion of galaxial volume with vast distances between them. When two galaxies collide, they literally pass through each other. However, the structures of the galaxies can be greatly distorted due to gravitational interactions, as seen in the spectacular picture above. Interestingly, what would intelligent entities thrived in those galaxies wonder about as they discover their galaxies' secret affair? :D
galaxy 1:"I've got a crush on you, sweetie pie."
galaxy 2:"I know it to my very core, hear me sigh...-_-#"
Credit: NASA, ESA, and the Hubble Heritage Team (STScI/AURA)-ESA/Hubble Collaboration
Acknowledgment: B. Whitmore (Space Telescope Science Institute) et al.
Source: http://antwrp.gsfc.nasa.gov/apod/ap061024.html