© Denzil Green
In North America these days, Cabbage is generally either eaten raw in Cole Slaw, or cooked using its leaves to wrap Cabbage Rolls. This is more the result of really only having one, dull variety of Cabbage available. In the UK, though, where there is greater variety choice, Cabbage is also sautéed or braised to act as a side vegetable which gives you a hot, cooked side veg while giving you the crunch and most of the nutrition of fresh Cabbage.
Red Cabbage and Savoy Cabbage used to be only well-known in the UK and Northern Europe, but are now slowly gaining familiarity in North America.
Red Cabbage and Green Cabbage have the most taste; unfortunately, the predominant one in North America is White Cabbage, which is really good just for Cole Slaw. This may be one of the reasons North Americans still aren't keen on Cabbage, as in their minds it's the flavourless, uninteresting White Cabbage.
Generally, the darker green the cabbage the more bitter and strong the taste - witness Kale and Cavolo nero. Medium-coloured ones are milder. Red and white cabbages are sweet by comparison with all the rest.
When buying, choose heads that are crisp, firm and well-coloured for their variety.
In autumn 2010, in response to an uptick in demand for cabbage, Tesco's in England began offering eight different kinds of cabbage, including Red Pointed, Japanese Flat, Red, Savoy, Sweetheart, White and January King. 
When shredding Cabbage by hand, quarter it first, and cut out the core. Press each quarter down flat and cut with a large knife. To crisp up shredded Cabbage, soak it in ice water with salt for about 15 minutes, then rinse and drain.
Compounds in Cabbage break down as it is cooked and recombine to form smelly molecules which include hydrogen sulfide (think rotten eggs). The longer it is cooked, the more of these molecules are produced, and the taste of the Cabbage actually gets stronger. Keeping the lid off during cooking also helps to reduce the smell, because then the sulphur release doesn't build up and compound in the pot. (Another thing that seems to work, for whatever reason, is adding a bay leaf or a tidge of French vermouth to the water.) A shorter cooking period for members of the Cabbage family is consequently good for both the taste and smelling senses, with the added bonus that fewer nutrients are lost.
A good way to cook boiled Cabbage: shred the Cabbage, boil in an uncovered pan. When it floats to the surface and is wilted, drain, dump out the water, then return to the pan with a tablespoon of butter, and reheat.
Red Cabbage will keep its colour when boiled if you add a bit of vinegar to the water.
A sprinkle of dill weed on cooked Cabbage really livens up the Cabbage.
To freeze: wash, cut into wedges. Boil 1 1/2 minutes. Plunge in cold water, drain, package, and freeze.
Freezing: Remove outer leaves from head. Cut in quarters, and cut out the core. Shred coarsely, or chop the head into thin wedges. Blanch shredded Cabbage for 1 1/2 minutes; wedges for 3 minutes. Plunge into cold water to cool. Then drain well, pack, and freeze.
Romans introduced Cabbage to Britain. Jacques Cartier planted Cabbage in Québec on his third-voyage there in 1541-42. British sea captain James Cook included pickled Cabbage as part of his ship's rations in 1771 to help prevent scurvy.