This year, the first day of Hanukkah coincides with Thanksgiving Day. Amazingly, this is the
first second time it's happened since President Lincoln established Thanksgiving in 1863 and it is also the last time it'll happen until the year 79,811. I'll say that again: after this year, Hanukkah and Thanksgiving Day won't overlap for another 77,798 years.
The reason is because the Jewish calendar is very slowly getting out of sync with the solar calendar, at a rate of 4 days per 1000 years (not bad for a many centuries old calendar!) This means that while presently Hanukkah can be as early as 11/28, over the years the calendar will drift forward, such that the earliest Hanukkah can be is 11/29. The last time Hanukkah falls on 11/28 is 2146 (which happens to be a Monday).
Update: As noted above, Thanksgiving and Hanukkah overlapped once before, in 1888, because Thanksgiving used to fall on the last Thursday in November and not the fourth Thursday.