This is an unpopular thing to say these days; one should say, "Happy holidays," so as not to offend anyone. I certainly don't mean to offend anyone; and when talking to my Jewish friends I wish them happy Chanukah; my chorus sings Ma'oz T'zur along with In Dulci Jubilo when we go caroling. In the rush not to offend, though, I think we forget that the original purpose of this greeting was to wish people well. To hope that they enjoy the season, however they celebrate it, as best they can.
The common "we must not offend anyone" mode always makes me think back to Aesop's fable about the man, the boy, and the donkey; you can find one version here. The moral of this fable is: try to please all, and you please none. If I wish someone a Merry Christmas, and they say, "But I celebrate Kwanzaa, we don't do Christmas", the only thing I can do is wish them a Happy Kwanzaa; if they choose to be offended because I didn't do that first, I can't stop them. I can see how people who follow other traditions feel overwhelmed by the tsunami of "Christmasness" that rolls over us every winter; but it still bothers me that I'm not supposed to wish them well without knowing in advance which particular form of well-wishing they prefer.
I'm not especially religious; and I hate to shop (although I don't belong to the Church of Stop Shopping either!). My view of Christmas is more Dickensian than anything else: I've read A Christmas Carol so often I know it almost by heart. Dickens' view of Christmas was only marginally associated with the worship of Christ; what he really valued it for was to encourage charity among men, especially charity from the rich to the poor ("to think of people below them as if they really were fellow-passengers to the grave, and not another race of creatures bound on other journeys."), but also from the poor to the poor; and sometimes charity was nothing more than to wish someone well.
So, with that in mind, I wish all of you well in the way that is most natural to me: that is, I wish you a Merry Christmas and a Happy New Year. If you prefer to translate that into some other form, feel free; as long as you remember the well-wishing.