I like the webcam idea! I'm home 99% of the time, but I admit that I'm always a bit worried when we leave for a couple of days. We do have insurances but there's some stuff that you cannot simply replace, like the old favorite guitars.
As for dogs, well, I've wanted to get one for quite a while. I don't think I'd actually let the dog out, but it could still scare thieves away and/or prevent me.
The reason those kids picked our backyard was probably that the blinds were practically closed, they saw no one inside and figured out that they could stay there for a while. They even had time to re-arange the furniture to sit closer to the wall not to be seen.
We were sleeping on the second floor, and my wife has this white noise thingie that she needs to sleep - I have a love/hate relation with that device because it drowns out the noises that I would need to hear to keep the place safe. Between that, the AC and the humidifiers, I'm having a tough time scanning for noises.
A dog could have acted as a helper on that one, even from inside the house. I'm thinking that the kids or any thief would have probably run away the minute the dog started making noise.