There's an old theory that the tides of history ebb and flow from the influence of Great Men. This theory, popular in the 19th century but today unwelcome in the halls of academe, is based upon the degree to which the actions of singular influential "historical heroes" determine how events played out. Going by it, the American Revolution was won by the skill and fortitude of George Washington rather than the logistical and strategic challenges which the American environment posed to a military accustomed to Old World combat. I can see, in some respects, why its fall from grace took place. Individual actors are not the only ingredient in the grand scope of history, and in many cases it doesn't make an incredible difference who's running the show.
This is one of the most critical considerations for any aspiring author of alternate history.
On the battlefields of the First World War, say, individual generals can be seen as caught up in the current of history and the dominating philosophy of the times, which reduced soldiers to so many pawns thrown away for little or no gain.
And yet, even then, there were individuals that nudged things the other way. Witness Sir Arthur Currie, commander of the Canadian Corps in 1917 and architect of the Battle of Vimy Ridge. If someone like Field Marshal Haig was in charge instead, I find it distinctly implausible that a more traditional British general would have taken the steps that won Vimy Ridge for Canada.
GURPS Infinite Worlds is probably one of the most dedicated sourcebooks on alternate history we'll get for a while, and it includes three lenses for game masters building their own parallel worlds. The first is that of the Great Man, as above. The second is the Great Moment, which gives the most weight to greater social forces - the example it provides is that if Adolf Hitler had died in a 1917 gas attack, say, the postwar situation of Germany was such that "Julius Streicher or Joseph Goebbels or some unknown street fighter might have become dictator and launched World War II and the Final Solution." The third is the Great Motherland theory, which draws a great deal of inspiration from Jared Diamond's Guns, Germs, and Steel, where history is based primarily on geographic factors and environmental adaptation.
Nevertheless, the Great Motherland theory is a blunt instrument if there ever was one, and is best suited for exploring the Grand Sweep of history; any closer, and it's like using a telescope for reading glasses. Bear in mind that a world in which western Eurasian civilization is dominant would, under this theory, describe our world and one in which Nazi Germany rules Europe equally well.
In my own opinion, all three lenses work, but at different resolutions of history. Right now, I'm working on an alternate history short where Pierre Trudeau was killed in 1968, jumping off the point of divergence I looked at in "To the Gallows" in January, and the question of how one man's absence would alter history is weighing heavily on my mind.
It wouldn't destroy Canada. Neither would it make it a utopia. Countries are bigger than individuals, even when those individuals lead them, and from a distance a Trudeau-less Canada in 2009 would likely be broadly similar to our 2009 in terms of population, wealth, industries and so on.
Getting closer, though, Trudeau shaped Canadian society to an extent that few others have, before or since. It was Trudeau that pushed through official, nationwide bilingualism and the National Energy Program - two moves that other Prime Ministers in his place might not have done. The culture of an Alberta that never asked for those Eastern bastards to freeze in the dark would, again, be broadly similar to our Alberta - it would take something on the order of global thermonuclear war to keep people from exploiting the tar sands - but would likely be noticeably different.
Furthermore, there's the issue of Quebec. There's no telling how a different Prime Minister in 1970 would have dealt with the October Crisis. The world is a fundamentally chaotic system, and from time to time individuals do have a long enough lever to move the world.
You may notice I used a lot of words like "possibly" and "likely" and so on in this post. For that, I only have recourse to S.M. Stirling, who quite rightly observed at a recent Worldcon panel that "alternate history is the ultimate non-falsifiable hypothesis."