My husband and I have a bike trailer for our toddler and she LOVES it. It is a great way for all of us to get out, exersize, get some sun, etc. We did a ton of research before buying ours as we were very concerned about safety.
The top of the line is the Chariot brand, which is what we have. The next best trailer is Burley. Both are much structurally safer than Instep or anything you can get at Toys R Us. They are both pretty expensive, but when it comes to safety, why skimp?
Both brands have single and double trailers. They each also have separate kits to purchase to turn them into strollers or joggers, and there is even a cross country ski kit. The one drawback with the Burley is that when you turn it into a stroller, the bike attachment does not come off, so it sticks out really far and can be a trip hazard for other people walking with you. The Chariot has a removable arm for the bike attachment that stows neatly on the side of the trailer. So, both brands are great, but the design of the Chariot is much better. REI carries both brands.
And finally, for safety, your children MUST wear helmets. In fact, in Oregon where I live, it is law for anyone under the age of 16 to wear one. There are small helmets for toddlers. Keep in mind that helmets are not to be used for children under the age of 1 as there neck isn't strong enough to hold up the extra weight of the helmet, especially in the event of a crash. Therefore, always have your kids (and you) wear helmets, but wait until they are one year old.
Good luck and happy biking!