I picked up a Burley at CyclovaXC a couple of weeks ago for taking my daughter with me on bike rides and we've both been really enjoying it. Of course, little Sofia wasn't all that happy the first time I put her in it, but once we started rolling she began to enjoy it.
The Burley rolls really well, but it's not like you can go out and hammer like when you're riding your bicycle all by yourself. It's tough in a headwind (because it has so much surface area), and you especially notice it when you go uphill, but most of the time you don't even realize it's there.
What I really like about it, is how compact it becomes when you fold it down. The above picture demonstrates how little room I have in my storage space, and, as you can see, the Burley folds up and tucks away nicely.
The other confusion people might have about a Burley is how to get it attached to their bicycle, but this too is easy and requires only five minutes or so.
First you take out the skewer of your bike wheel. The skewer is just the little rod with your quick release lever on it. Take this off by unscrewing the end without the lever and simply sliding it out. Be careful when you do this because there are two conical springs in the skewer and you don't want them to fall down into the grass where you might lose them.
Once you have the skewer off, you can slide the Burley latch assembly unit onto the skewer rod (see the above picture). Once that's done, put the first conical spring back onto the rod, slide it through the axle of your wheel, and then put on the other spring and bolt it.
When you're finished, it should look like this. All you have to do is tighten your quick release skewer and you're ready to go! The Burley latch assembly just lives on your bike after this, so it's a one time operation. It's very easy and convenient, and it allows you to combine your exercise time with your day care time!