Traditionally the Hamburg Christmas Markets open on the first Monday after "Totensonntag" (Sunday in commemoration of the dead ) - and there's loads of them.

The biggest downtown Hamburg Christmas Market is the traditional Roncalli Weihnachtsmarkt at townhall square (Rathausmarkt). Advertising with "Kunst statt Kommerz" (art instead of commerce) this Christmas Market claims to be a little different - and it will in fact make the kid's hearts beat faster at the sight of the "Spielzeuggasse" (toy-alley).
Of course this market also offers the ubiquitous booths for Bratwurst and Glühwein. If you fancy a Glühwein after work, go there early - after office closing time all the markets in city centre are PACKED.

Slightly off track, but (fortunately) not as crowded as the other markets: Fleetinsel market between Stadthausbrücke, Alter Steinweg and Rödingsmarkt (near Steigenberger Hotel and Ständige Vertretung).
This market opens for the second time only and is therefore not yet so well known, nevertheless very nice with pagoda booths and has a charming maritime touch as you can tour three oldtimer sailing-boats.
There will be a cultural supporting programme offering e.g. readings at the wintergarden of Steigenberger Hotel by local cultural figures such as Hans Scheibner, Carlo von Tiedemann and Bernhard Lahsann.
Fancy ice-scating in the middle of town? Then visit the new christmas market on Jungfernstieg which will be there for the first time this year.
The company of a friend of mine are organising this market and it definitely will be the most cutting-edge christmas market in town.
Christmas markets will be open daily from November 27th to December 23rd, 11 a.m. to 9 p.m. (officially). Here's a map of all christmas markets.
Enjoy your Glühwein!