In both Tunisia and Egypt, the main demonstrations were preceded by desperate individuals publicly setting themselves on fire as a protest against the hopelessness of their lives, or their treatment by their respective regimes.
In Tunisia, the first person to do this was on December 17th, but it took until January 4th for him to die. Protests built over several weeks, until President Ben-Ali was obliged to flee the country on January 14th.
In Egypt, the first self immolations were on January 19th, and now, 12 days later, although the outcome is uncertain, the regime hangs by a thread.
So far, there have been two self-immolations in Saudi Arabia: a 60 year old man on January 22nd, and a 42 year old on January 25th. So far, demonstrations have been limited to a few hundred people (video here) in Jeddah, mostly protesting that the government had failed to prevent devastating floods there. Demonstrations are not allowed in Saudi Arabia, and the authorities arrested tens of the protesters. I am not presently able to find any evidence of the self-immolations leading to further protest (feel free to provide any further links in comments).