The main reason you might be worried about looking for your driver's license number is probably that you have lost the card, and you probably are in need of it for other purposes. However, getting your driver's license number back shouldn't be something to worry about as you can get it through other records.
What you should do first is to check if you can locate any expired driver's licenses of yours. If you are able to find one, it should contain the same number as your current license number, but the two must have come from the same licensing agency. You can also get your license number through your vehicle registration.
A number of times, your license number will be required as part of your vehicle registration. Also, many don't know they can get their license number through their financial records. Finally, you can simply contact the licensing agency that issued the license number to you to retrieve it.