To clarify:
ID Cards in Germany (and presumably in many other continental European countries) are simply a "Passport Light". For example, in Germany, you are not required to have an ID card if you have a passport. It is also an urban myth that you always have to carry it with you. You only need to possess either a passport or an ID card.
ID Cards can be used for travel within the EEA (= EU + Norway + Iceland + Liechtenstein) and Switzerland. Additionally some popular tourist destinations such as Turkey or Morocco do not require a passport from German nationals, but only an ID card.
The German ID Card is a lot cheaper than the German passport, a lot lighter and a lot easier to carry. Personally, I find it a lot less intrusive having to show an ID card when, e.g., opening a bank account than having to come up with utility bills, bank statements and other idiocies like that. The ID card only contains my name, my picture, my date and place of birth, my height, my eye colour, my address and an ID card number (which changes every time you get a new ID card).
I do not really understand the reluctance of the Brits to such an ID card; I however do understand the reluctance of having all data pooled in one big database. I can just imagine a civil servant forgetting a copy of the entire database on a data stick on a train at some point in the future...