We've adopted two dogs, one from a German Shepherd rescue group and one from "Mingle with the Mutts" at our local pound. Both were smart, healthy, active and great with kids. I've never adopted from this group, but as a GSD fan, I admire their efforts, www.dogshope.com
I am a volunteer for CHA Animal Shelter in Westerville, and we have some fantastic dogs. What are you looking for? I also have lots of contacts in the rescue community. I have a wonderful American Eskimo dog foster right now.
On petfinders there are many shelters listed. All you do is put in your zipcode, what animal, breed, sex. Then there they are ! Nice photos and info on all the adoptees.
I think that Rescue is a great way. Many breeds have their own Breed Rescue. Make sure that the dog in question has been in foster care, and all basic medical issues have been taken care of. A good rescue will be very responsible in place a dog.. and should concentrate on matching each dog with the right family.
SICSA on Wilmington Pike in Kettering has a nice adoption program. I believe they offer free obedience classes for their clients as provide follow up assistance if you have questions / concerns with your dog. Also, don't know what type of dog you are looking for but there is a beautiful Aussie at the Greene County Animal Shelter. She was found with a collar and leash but apparently has been there over a month. Good luck!
I belong to The Miami Valley Labrador Retriever Club. We have a rescue group we support that has some wonderful Labs (and wanna be Labs). There is also a Lab Rescue in Dayton. Most Rescue groups from all breeds are good places to go. They are usually supported by experienced breeders. The dogs are usually good dogs that were mishandled or not able to be kept by their previous owners.