Emily - I live in Arlington, VA and the county has a very, very strict leash law. In addition, DC and Fairfax County (which surround Arlington) have similar laws. I've encountered a "problem" off leash dog only once so far---more of a "obstacle" than a threat. I pass a lot of dogs and their owners when I ride and I make it a point to say "Hi puppy." I'm a big dog lover, as I have three beautiful golden retrievers.
I completely understand your fear of loose dogs, however. A couple years ago, I was walking Agnes (my big girl--96lbs) in our neighborhood and a vicious dog attacked Agnes, dragging me and the dog's owner across the street (talk about major road rash). Yes, both dogs were leashed. I thought the dog was going to kill Agnes, so I kicked the SOB. Ended up that I was the one w/bites and Agnes got off without a scratch. I preferred that outcome, if one of us had to be injured. Anyway, I won't walk my girls anymore because of the irresponsible owners who insist on having aggressive dogs whom they won't control. I don't live in the "hood," either, so who knows why yuppies need these beasts? Thank goodness I've never had one come after me while I'm biking. Sometimes, if you just scream at them--GO HOME or NO, they turn tail and run (so I've heard).
Arlington is an urban area and I limit my street/road riding. We have an awesome system of paved trails in the DC/MD/Norther VA area--it's a good thing because a lot of the drivers here aren't "bike friendly." Also, it's crowded beyond belief here and there are way too many people who live in the DC metro area. It's changed a lot in the 18 years I've been here and it's not for the better. 13 more years til I can retire and move somewhere less crowded, with weather conducive to year round riding!
I really miss Pittsburgh, PA, which is my home town. People are nice there.