I have a road ID on my shoes. I also carry my DL, a credit card, a copy of my insurance card and some cash (If I can find any!) in a Jimi in my jersey pocket. As soon as I get back from a ride, I toss it in my purse because I have been caught without them more than once when running an errand after biking!

This is the Jimi - it keeps my sweat from yucking up my stuff.

http://www.thejimi.com/wallet/index.php

I don't think it's a requirement to have a photo ID on you at all times, but its certainly a good idea. It seems a bit weird that the cop would ask for a DL if you aren't driving though.