You need to assess the risk, taking into account the very low probability of having your identity stolen and the fairly low inconvenience, against the time and effort it takes to take protective measures. Don't live in fear of it.
That said, the single best way to protect yourself from random ID theft is to use a decent bank with good fraud protection. In the UK, Barclays and HSBC are very good, Natwest and Halifax are very bad. Citibank is a bad US one.