I have no problem hunting right up against the property line, but I won't shoot across it or cross it myself without permission. I'm really big on property boundaries--I am very respectful of others' property, and I expect others to respect mine--but I see no reason to use less than the full property I'm allowed to access. If I bought a 100-acre farm, I'd expect to use all 100 acres, no more, no less.
The kicker is if you have a neighbor who won't let you track deer onto/across his or her property. In that scenario, I'd probably back off the property line a bit and give a buffer, but that's for my own good, not the neighbor's.
If you know the neighbor hunts, introducing yourself and trying to form a QDM coalition or just establish rapport can pay HUGE dividends when the blood trail of the monster buck you just shot leads you off your property on a midnight tracking job--really pays to know ol' Joe and Sally Smith's phone number and be able to get permission to recover your deer.