We have a very large pasture for the hens out on our farm. ~15,000 square feet. We do not cover the area, nor do we have anything to keep critters from digging under the fence. There are coyotes, foxes, and coons galore, but they generally do not come in close and I've never had anything burrow under the fence. We have lost a bird here and there to Great Horned Owls, generally very late in the evening, but it's quite infrequent. We don't have any neighbor dogs that bother us. The only one that comes around is a big brown lab and he's been trained to leave chickens alone.
We had welded wire fence around the entire pasture and still have a few section of it, but it generally doesn't last more than a few years. The bottom wires rust out from ground contact and more generally, the welds start coming apart. With lawnmowers, weedeaters, and kids banging into it just starts to come apart. With 2x4 openings it only takes a few loose vertical strand before the hens can run through or a dog can get in. There were sections that came apart so bad that a dog could run right through (our biggest problem was just hens running everywhere, if there is a hole big enough to get through they will find it). The bad sections that we still have have been layered over with various pieces of fencing and chicken wire. The rest was replaced with 2x4 knotted, heavy gauge, six foot tall horse fence. With new 8' t-posts every 10 feet it was rather expensive, more than $3 a running foot, but I expect it to last for decades. This is what I used:
http://www.redbrand.com/Products/HorseFence/Non-Climb.aspx
Here is a photo I posted in another thread this evening, you can just make out the new fence: