I've been in January the past 2 years, and am going again in '08.
2006: Arrived on January 1, stayed for 5 days. The 1st & 2nd were pretty busy, but it really died down after that.
2007: Arrived on January 6, stayed for 6 days. The 6th & 7th were marathon weekend and were packed! Also, the roads and transportation for WDW are nuts for that weekend. The following days were pretty busy too with marathon runners and their families staying for vacation.
2008: Arriving on January 6th, staying for 6 days. I really believe this won't be a very busy time. It is several days after the New Year Holiday, and I'm leaving on the 11th, the first day of marathon weekend. The last day may get a little busy with marathoners coming in, but the rest of the week should be great.
Weather is fine in January, a little cool in the mornings (but not too bad). You might get a little rain, but not enough to mess up your trip.
The down side of January: January is a month they use for rehabs on rides, so a couple of biggies could be closed when you're there. This year, Splash Mountain and the Rock n' Roller Coaster were both down for the month.
Also, the parks have shorter hours. But the smaller crowds allow you to do more in a shorter amount of time.
Enjoy your trip, whenever you go.