In the immortal words of Lex Luthor: WRONG!!!
Joking aside, snooping is always, always wrong, and it's one step below cheating in the relationship-ending category. Yes, even if you were right to snoop and he is doing something wrong. Snooping is both a violation of somebody's privacy and a flat-out statement that you have no trust in them to tell you the truth.
Imagine how you'd feel if you discovered your boyfriend was going through your email, or calling your work pretending to be someone else just to see if you were really at your desk like you said you were. Freaked out and angry, right? So will he when he inevitably catches you; snoops always get busted because they just keep doing it.
If your boyfriend is doing something that makes you feel weird or worried, don't pussyfoot around it: ask him point-blank. Give him an opportunity to explain what's going on. If he doesn't have a good answer, you can decide from there.