bierluvre-Border Terrier
FatMan-People have covered a lot of the basics here. Another book I would add to check out is "Before you get your Puppy" by Ian Dunbar. It's got a lot of info you'll want to know before you even bring the dog through the front door. The underground fence can be extremely effective if you train well. I have a friend who's dogs will not cross the line for toy, rabbit, squirrel, or even with the owner calling. THis is with collars on or off. She took two weeks of walking the perimeter on leash with the dogs so they could hear the tone and she would correct them and say "no!" She did this every day several times a day for two weeks. Then she walked them up to the perimeter and let them get shocked (also on leash) so they knew the consequences. SHe still occasionally retrains and they are never left unattended in the yard. But they can be off leash now with no concerns. And as everyone has said, anything and anyone can still come into the yard with your dogs without a physical fence. Now, if you never leave them alone in the yard this isn't too much of a problem.
Certain breeds like the sight hounds (greyhounds, salukis, afghans etc) should never be off leash without a physical barrier. They are just too prey driven and all of their focus goes on the prey. (of course there are acceptions to every rule but you won't know if you have one until it's too late!) The northern breeds aren't for beginners for soooo many reasons hair, pulling, barking/howling, more difficult to train etc. The extra hair is one of the reason's they are hard to train to the e-fences, it's hard for the prongs of the training collar to reach thru the fur and have any effect.
Someone mentioned a greyhound, Not a bad dog for someone who hasn't had one in awhile. They are the 40mph couch potatoes. As I mentioned they really can't be trusted off leash unless they are in a fenced area.
Some of the smaller dogs that were bred for companionship are great too. (Think Shih Tzus, Pomeranians, Cavalier King Charles Spaniels, Maltese) Every pure bred comes with it's own set of health concerns and just because it is a little dog PUHLEEEESE don't think it doesn't need to be trained. A little dog that pulls is just as annoying as a big dog only it's a little less tiring.
Certain "popular" breeds are experiencing some serious behavior problems. I would rather have my two year old approach a Rottie or a Doberman to pet it than a Cocker Spaniel or a Dalmation. In my experience (I've worked in animal hospitals, kennels, and doggie daycare facilities all my life) these can be some of the most unpredictable/nasty breeds encountered.
Certain breeds will cause your home insurance to skyrocket or drop you like a hot rock. (Think bully breeds, dobermans, german shepherds, rotties etc)
Herding breeds can be good if you have the time to invest. I had an Australian Shepherd that would allow my girls to use her for a step stool without a backward glance but she learned how to let herself out my front door whether the safety hook was on or not. They need to have huge amounts of physical exercise, and if it was rainy for three days in a row she got crazy. Beyond the physical the herding breeds are smart dogs, and will need tons of mental stimulation. That is why they are easy to train, but they will need something to do for the rest of their lives.
My suggestion would be to go on the AKC website and read up on different breeds that appeal to you. Even if you aren't going to go with a pure bred and prefer to head to the pound, at least you'll know some of the characteristics your mixed breed may have. (that is assuming the shelter people can tell a shepherd from a lab and lots of them can't!)
Make a prioritized list of things that are important to you in a dog and try to find one that meets your top three, top five would be perfect.
Check out
www.petfinder.org for available animals in your area.
Look on
www.akc.org for dog info and dog shows in your area. Stop by a dog show and approach anyone who's wandering around with a dog you are interested in. 99.8% of dog owners at a show will talk to you about their breed until you want to slap them. Just make sure they aren't getting ready to go into a ring to show or something first.
If you decide you want a pure bred check out the rescue orgs for that breed first. They can get you a dog who's temperment and behaviorial issues (if any) are well known.
Feel free to come back here for more info or PM me. Lots of people on here with great info!