Actually, Disney now splits the race weekend, so the 1/2 marathon and the 5K & kids races take place on Saturday and the full marathon takes places on Sunday.
We've been there twice at this time of year, and usually arrive late the week before, then stay for the week after. Our dates this year were the same as the above poster's --the 5th thru the 13th.
I will say that the crowds will be appreciably low, esp during the week after the marathon, most runners leave afterward, some stay but Jan crowds are pretty low anyway. The longest wait we had during our trip was during an EMH night at Epcot for Soarin, probably 20 mins or so.
Also, just an FYI, while some are saying the marathon doesn't affect thing, you need to know that they do have road closures in place around WDW to accomodate the runners. The 1/2 marathon runs from about 6am until 9: 30 or so Saturday and in the full, runners can take up to about 7 hours to finish. Traffic was sluggish on those days, and depending on where you were going, it can be delayed a bit. The marathon ends in Epcot's parking lots (i think this is the case this year as well) and so there are many spectators and runners in that area getting bussed.
I would not avoid taking a trip because of it, just wanted to mention this so you are aware of the potential slight delays that might occur.