New Hampshire has an interesting way of reporting voter registration, apparently because they allow same day registration and voting - they only report after primaries and general elections. This means that the only registration available to compare to previous years is as of the January primary. A lot can happen between January and now (or November), but let's see what trends there were anyway.
In 2004, Republicans had a sizable registration advantage during the primaries of 246,529 to 199,386 for the Democrats. By the time of the general election, they still had a very sizable advantage: 267,141 to 228,395. Independents were the largest group, totaling 360,325, and they seem to have swung appreciably toward the Democrats, as Kerry won by 9,000 in spite of the 39,000 Republican registration edge.
In 2008, Democrats cut the Republican edge in registration considerably during the primaries, down to about 12,500. By the general election the Democrats had taken a narrow lead of almost 2,000 in registered voters, and in the actual election, Obama won by 68,000.
In 2010, Republicans had gained a tiny lead in registration during the primaries, and pushed it up to about 8,000 for the general election. In spite of this small advantage, Republican Kelly Ayote blew out the Democratic nominee by over 100,000 votes, 23 points.
This year, Republicans re-established their dominance in registration in the primaries, pushing it back up over 43,000. Clearly, this year's election looks to more closely resemble 2004 than 2008. The question is whether the undeclared will continue with their recent lean toward the Democrats during the presidential elections, or whether they will maintain their strong 2010 swing toward Republicans. Given the registration advantage, this seems to be a toss-up at worst for the Republicans.
UPDATE: Realclearpolitics.com today moved New Hampshire from their 'Toss up' category to 'Leans Democrat' on the basis of a new poll showing Obama up by 15 points(!). This is a perfect example of ridiculous polling. As shown above, since 2008 New Hampshire has trended strongly towards the Republicans, yet this poll purports to show that Obama is going to beat Romney by 5 points more than he beat McCain. Looking at the internals, their sample consists of 323 Obama voters compared to 216 McCain voters - almost exactly 3:2. In the real world, Obama beat McCain 54:45.