According to Wikipedia, New Hampshire has been having competitive presidential primaries since 1952. During that period there have been 14 Democratic presidential primaries. Of those 14, three were not seriously contested. Those three were the 1960 primary pitting John F. Kennedy against a businessman named Paul Fisher. The 1964 primary pitting President Lyndon Baines Johnson against what Wikipedia describes as "no serious opposition." The 1996 primary pitting President Bill Clinton against what is again described as "no serious opposition." That leaves 11 primaries that were seriously contested.
Of those 11 primaries, the ultimate winner of the Democratic nomination only won four of them, the 1976, the 1980, the 2000 and the 2004 primaries. In the other eight times, the winner of the New Hampshire primary didn't win the Democratic nomination. Using a percentage analysis this means that only 36.3% of the time has the winner of the New Hampshire Democratic primary won the Democratic nomination.
What about the Republicans? Among Republicans the winner of the New Hampshire primary is more likely to be the ultimate nominee of the Republican Party. New Hampshire has been holding a competitive Republican primary since 1948. This means that there have been 15 Republican primaries. Of these 15, four of them have not been seriously contested. Of the remaining 11 primaries, the winner of the New Hampshire Republican presidential primary has won the Republican nomination six times. Again using a percentage analysis this means that 54.5% of the time the winner of the New Hampshire Republican primary has gone on to win the Republican nomination.
All of these is not to say that what happens on Tuesday, January 8, 2008, isn't important for both parties. It is to say that statistically speaking it is more important for the Republicans than for the Democrats.
One thing that makes what happens Tuesday in New Hampshire a little less important in terms of who wins the nomination of either party is the fact that both likely second place finishers, Hillary Clinton and Mitt Romney, have the resources to keep their campaigns going until at least February 5, 2008 if not beyond. In the past a poor showing in New Hampshire resulted in a drying up of campaign funds. Assuming that Clinton has not spent all her money in New Hampshire and Iowa, she should have enough money to continue and certainly Romney has enough money to continue.
It will historic if Obama wins New Hampshire and it will be important if John McCain wins New Hampshire, but in neither case will it end the battle for either party's nomination. In the case of the Democrats, the winner of the New Hampshire has a better than 50/50 chance of not being the Democratic nominee. This means that Democrats and Republicans in other states will get a chance to say who gets their party's 2008 presidential nomination.