My parents have had their system (Invisible Fence) for probably 6 years now. We have a beagle and an entlebucher mountain dog (little sister of the Bernese and Great Swiss). They both figured it out very, very quickly. The Entle respects the fence and knows exactly where the limit is. I don't think she ever challenges it. Our beagle however gets right to the limit of where it starts to beep at her. Mainly that's because she's a beagle and follows her nose and then her brain.
The beagle has gotten through the fence a couple of times, but they have been our fault (dead battery, circuit that the fence was on is tripped, loose collar). For some reason our beagle detests Wheaton terriers and will go nuts if they are on the sidewalk. She gets pretty close to the fence but that's about it.
We love the system, but you have to remember that it's not foolproof. Most issues are maintenance (batteries, making sure the collars fit properly after the dogs loose their winter coats and weight, cut line from aerating or gardening. Something we did was have the lower half of the driveway be off limits that way someone can pull in without having to worry about the dogs.
Few minor issues that we've had:
-knicked the line while aerating. We marked the line ourselves and we were off. If you ahve the invisible fence guys come out and mark for you, they will cover the cost of the repairs if they were wrong (i.e. they were off and not the fact that the guy aerating used the flags as a slalom)
-one of our dogs had her collar fail. we took it in and they replaced it on the spot. no fees, no nothing. apparently they are guaranteed for life.
-paths. our beagle patrols the perimeter of the yard every time she goes out and we now have paths marking where the fence is. We also have a less noticeable path in the backyard on the far side of the fence where the rabbits and squirrels detour around our yard.
-if the power goes out, the fence goes out. Unfortunately it's difficult to tell if the power is out on that circuit as it serves the outdoor plugs and garage.
-remember that it is not a baby sitting system for the dogs! You still need to just make sure you know where they are. If you hear lots of barking and yelping, the dog may have gone through the fence or something had come through the fence and is bothering the dog.
That said, we love our and we couldn't live without it. Especially with how high energy our dogs can be.