I took Lucy on a short (~2 mile round trip) ride to the local park and back, using the milk-crate I attached to my Bike Friday Tikit's double front rack with bungee cords (as shown in a previous post). Worked like a charm, cost me nothing (since I found the milk crate in a pile of stuff my neighbor was going to put in the recycle bin, and I already had the bungees), and it's easy to attach and remove. Perfect size for Lucy, who weighs about 17 lbs. I bet I could fit a slightly bigger dog in there, though.
My point-of-view when stopped at an intersection. I laid a couple towels down to as a cushion for Lucy to sit on. You might notice a slight skew comparing the handlebars to the crate. That is actually due to the handlebars being slightly misaligned, which I hadn't really noticed until this ride. Took 30 seconds to re-align them using an Allen wrench. The crate itself is quite stable with 5 taut bungees holding it in place, and doesn't shift around.
At the park. I could attach the crate to the rear rack, but I like having the dog up front to interact with, and I'm pretty sure she would get antzy in the back as well.