We started out with a Bobike Mini front-mounted seat. It was great, but there's a limit to how big a kid you can carry in front of you, and how comfortably you can ride with one of them in the way. It's a short trip only proposition... which is fine, because that size of kid is only up for short trips on the bike.
We then moved on to something similar to this one that I randomly selected from evilBay:
http://www.ebay.com.au/itm/BABY-TODDLER ... 3ccbb7710f" onclick="window.open(this.href);return false;
It mounts on the seat tube, with the kid supported by a pair of long cantilevered spring supports. I can't recommend this approach highly enough.
It's much more comfortable for the child, as they're somewhat isolated from road surface shocks. With a rigid rack mount, any bump your rear wheel goes over is going straight up your kid's back.
I wasn't too keen on the rear-mount at first, thinking that my daughter wouldn't want to spend that long looking at my bum, but once I gave in and got one, we did a heap of riding together. Aside from the couple-of-days-a-week childcare drop-offs (on my way to work - I attached my pannier to a front low-rider rack), we did some big recreational rides.
The longest ride we did was 85km in a day, when she was 3 years. To do a ride like that is more a challenge of parenting skills than it is a challenge of your cycling ability. Not to say that a day ride with ~15kg of live luggage isn't a challenge, but it's a long time to keep a kid entertained. We did lots and lots of talking and singing and joking, working through the many hours it takes to ride that far (with adequate rest stops), and always had the option of bailing out and taking a shortcut home (or calling for a sag wagon ride in case of meltdown). But she kept telling me to take the long way, so we kept going.
We also did a 50km rail trail ride, on 28mm road tyres... not something I would recommend with a rigidly mounted seat, but on the cantilever mount, she just floated over the gravel yelling "faster faster!". Another one we don't talk to Mum about was the time we hooked in to the draft at the back of a pace line on a gentle downhill, and held 55km/h for a couple of km
You'd want a pretty sturdy bike to mount one of them on - it's an abnormal stress load for the seat tube to take. Mine was on a Surly Long Haul Trucker, which is nothing if not a sturdy bike. Probably not something you'd do to a carbon race bike... even if the clamp fit.
Now we're on to the trail-a-bike stage. It's harder work for her, balancing on a bike seat, so we've cut down the length of rides we'll attempt. It's also harder work for me
. She's done a couple of 35km days (and lots of childcare runs), and loves it, but it's a different kind of riding. I suggested she gets back on my bike for a longer ride every so often, but she won't have a bar of it now she has her own pedals...
tim