The Islamists responded by launching an armed rebellion. It turned into a decade-long civil war in which both the Islamist rebels and the "le pouvoir" used terror against the civilians caught in the middle. At least 100,000 Algerians were murdered, the regime finally won in 2002, and the population was so scarred by this experience that it has remained submissive – until now.
The current wave of protesters are on a roll, but getting rid of Bouteflika is just the first step. The interim leader who has to organise a new election within 90 days, Senate president Abdelkader Bensalah, is a regime loyalist and a close associate of Bouteflika. And the generals and powerful businessmen who really control the regime are still hoping that a change of leaders will be enough to send the protesters home.
It won't. What's really driving this youth-led revolt is desperation: one-third of the country's under-30s are unemployed. The regime can no longer buy them off with cheap public housing and subsidised jobs because oil revenues have fallen steeply, and they are too young to remember the horrors of the civil war.
Since the under-30s are two-thirds of the country's population, they are probably going to win. Having been in power ever since the end of Algeria's war of independence from France in 1962, "le pouvoir" is now going to be dismantled. The question is what happens next, and nobody knows.
The precedents elsewhere in the Arab world are not encouraging. When Egyptian dictator Hosni Mubarak (29 years in power) was forced out of power by popular protests in 2011, the Muslim Brotherhood won the subsequent election, but the army overthrew them in a very bloody coup and is back in power. The attempted democratic revolutions in other Arab countries also mostly ended also ended in disaster.
When Libyan dictator Muammar Gaddafi (42 years in power) was overthrown and killed in the same year, there were no free elections, and the civil war started right away. Most of the contending groups are Islamist of one flavour or another, and the war is still going on.
When Syrian ruler Bashar al-Assad (18 years in power) faced a challenge from pro-democracy protests in 2012, he was not overthrown, but the civil war that ensued has destroyed half the country and is only now coming to an end.
So why would anyone think that Algeria can do it better?
One reason is that most of the young in Algeria really aren't Islamists any more. Generational turnover has done its work, and the current youth generation is mostly secular, pro-democracy, and animated by non-violent ideals.
But that's about it. There aren't many more reasons to believe that Algeria will turn out differently second time around, and there are lots of reasons to fear that it won't be different this time. Yet hope springs eternal.
Tunisia managed to turn itself into a democracy non-violently in 2011, and despite huge unemployment among its under-30s it still is one. It's hard to see how freeing Algeria from the dead hand of a superannuated dictatorship will really change the grim economic prospects of its younger generation – after all, that hasn't happened in Tunisia after almost a decade of democracy – but it's worth a try anyway. Despite the risk.