In the years that I've been exploring, I've spoken with many people on the topic. The reactions range from, "wow! that's really cool!" all the way to the opposite end of the spectrum, "you're trespassing hooligans and taggers".
I couldn't disagree more with those latter comments. Yes, as with anything, there are exceptions. But for the most part, if you take a look through any UrbEx site, you will see the same philosophy echoed almost to the point of cliche...
Take only pictures, leave only footprints.
This is something I truly believe in. Yes, in the letter of the law, some explorations constitute trespassing. Some more than others. But if you think for a moment, why do we have trespassing laws? Because people damage the property of others and we don't want that. A second reason is liability. If we do due diligence in attempting to keep people out, and they get hurt on our abandoned property, we can't be held liable for it.
Idealistic as this sounds, if no one broke or vandalized anything, took responsibility for their own stupid injuries when exploring something unsafe, would the owner actually care? I don't believe so.
As with any ethical debate, different people stand in different parts of the spectrum. Some folks believe it's ok to take plywood off a building to gain access. Some believe that the odd souvenir is ok since it's all just junk the owner left behind.
I'm not here to pass judgement on those people though I, myself, do not consider those acceptable for me. If we followed rules so closely, we wouldn't be explorers, would we?
So, I explore, sometimes past the line of trespassing, always with careful eye on where I place my feet, always careful to leave everything just as I found it.
Then others can enjoy it as I have.