I snooped once many many years ago, because I felt he was being dishonest. He was, but I didn't confront him about it. I felt awful for snooping into his business, and still do. I feel that people will tell me eventually, as he did tell me eventually. I haven't done it since. It was immature of me, and probably because I had low self-esteem at the time.
If you leave the lines of communication open and you are stable and honest as well, they will tell you what they were originally hiding from you.
The problem is that most men hide things because they have to deal with irrational and overly emotional women. It's a cause and effect thing. If you are on the level and not a source of drama, as well as a good listener, I think that men will tell you when there is something wrong. My husband tells me when there is something wrong or something I can correct about my behaviour. I do the same for him.
Case in point, a few weeks ago I was PMS'ing and feeling a bit cranky. I explained to him first thing that day that I was feeling a little emotionally unstable and if I was responding oddly to him, it was because I was feeling a little vulnerable and unstable. A few days later he asked me to deal with our thirteen year old because he was feeling short-fused and overly frustrated because he hadn't much sleep the night before.
If you communicate on an honest level and if you allow each other to feel secure in being honest, then you have no reason not to trust them.