In countries which implement ID cards, just knowing a person's unique ID number doesn't help a bad guy. In fact we freely give out those numbers when shopping when we need an invoice for accounting purposes, at the doctor's, for civil registry purposes (recording of marriages, children etc.), at the bank and so on. The number is just a convenient method of tracking a person in the records.
But don't confuse the number with [i]proving your identity[/i]: you have to present the card in person (it's a picture ID card); people are protective of their ID card; the cards have safety elements which make forgery very hard; there are automated verification machines (used mostly by banks and country border routine checks) which scan a card and respond back within seconds if it's valid.
So yes, identity theft is practically unheard of in Europe, in the sense it's used in the US. For example, in order to get a loan you have to show up at a bank and request it in person, physically sign a contract and wait (days) to be checked out. An impersonator would have to (a) forge an ID card; (b) forge your signature on a contract; (c) hope no word of this gets back to the actual person during the check-up period. And even if they manage all this, the laws are such that once it's proven it wasn't you, you're completely off the hook.