One thing to keep in mind is that wood pigeon is totally different to common pigeon found in cities (actually, they're rock doves; not pigeons at all)
Very clean birds, lean meat and really tasty. Usually sold as crowns rather than whole birds, there isn't much meat on the legs. But if you do get whole ones, keep the rest of the bird for stock; great base for soup.
I love wood pigeon and have it whenever I see it on the menu.
I last had it the Harwood arms with broad beans and soft oatcakes and it was one of the best things I've ever eaten.
If you like other game then you should in theory like pigeon.
A word of warning though it has very little fat and can dry out very quickly, in unskilled hands it can become like leather.
Actually I don't find it too hard to cook, it doesn't really require any fancy cooking method, just be judicious about cooking times. The danger is cooking it through to well done, in which case it will get unpleasant and leathery.
To get it blushing red is all you need to do. Say remove the breasts and literally flash cook them (1 minute on each side), or do as in St John - brown whole bird on all sides (although as little as possible on the breasts), knob of butter inside, roast for 10 mins in a really hot oven, rest upside down. Lovely. Best of all its a nice, cheap, healthy meal you can cook for one person.
Everyone SHOULD eat more pigeon.