I'm kind of reminded of the board game Civilization (the one the computer game is very loosely based off of)...
In that game, much of how you advanced your civilization was through building cities to get trade cards, which you could use to purchase technological advancement. The problem is that, mixed in with the trade cards, were disaster cards. Especially in the "Advanced Civilization" expansion pack, there were something like 20 different disasters in 9 different decks of trade cards, and you typically drew one card per player from at least the first 5 decks per turn, meaning you typically saw at least one disaster card per player per turn.
Because of this, you generally had to play your game based upon the assumption that every given turn would involve something like an earthquake or a flood or a civil war or an Iconoclasm and Heresy card would pop up and wipe out at least two cities a turn - which actually isn't too hard if you are prepared, it just means you keep population tokens ready around the city sites so that when the city vaporizes, you have enough people to rebuild it the very next turn.
In fact, because you have tax revolts if you have too many population tokens on the board, it's actually useful to make sure you get hit with a disaster, just so you have something to sink some extra population into. (Unless of course you're just starting a war for shits and giggles against your neighbor. That's always a great way to get rid of extra population.)
AAAAANYway, I would have to say I like the idea of some random disasters, but like Dutchling and others have been saying, it would be better if the "random bits" were more indirect causes of civilizations or cities collapsing than simply rolling a 5 on a 1d100 roll.
Right now, we have cycles of famine and plenty in food production, which is capable of causing periodic city collapses, but where there are more variables in play than a simple percentile destruction of a city - there are food stores and dependencies that the cities have upon villages, and cities aren't entirely wiped out, but are mostly just reduced.
Having some sort of set of variables for civil unrest would be fun, where you could randomly roll that the new king is really unpopular with the people for spending all his time with the nobility, but oppressing the people (nobles unrest -10, popular unrest +15), and then having a spike in food prices (popular unrest +20), and having a war that is starting to turn against the king (nobles unrest +10, popular unrest +10) leading to a popular uprising that the king has to send in the army to quell.