For going away for cheap I am a big fan of L'Tur. They are a travel agency specialized in last-minute deals. I'm especially fond of their deals on flights to popular holiday destinations. You can usually get very cheap flights to Egypt, Morocco and other places around the Med with them as well as find some great offers for long-distance flights to Africa, India, Mexico and South East Asia.
If you are limited to the Christmas holidays exactly L'Tur might not be the best choice (they will only be able to sell the left-overs), but if you can leave about a week before Christmas they might have some great deals.
Destinations that are warm enough for a beach holiday around Christmas are the Canary Islands, Spain and the Red Sea area in Egypt, specifically Hurghada and Marsa Alam.
BTW, if you are on a really tight budget keep your eyes peeled for 1-week trips to Turkey. During winter there are special offers to Turkey sponsored by the Turkish ministry of Tourism. The price is usually from 99 EUR per person if two people book at the same time for the flight and a week in a 4-star hotel with half board, some excursions to Antalya and Pamukkale. That can be a great deal if you like culture and shopping and don't mind 10-20 C mixed in with some rain and a beach too cold for a swim.
[ Edit: Edited on 04-Nov-2009, at 08:08 by t_maia ]