Now I know the cliché thing everyone will almost always say is, "If you need to checkup on your SO, then that means there's no trust, and trust is the foundation for a healthy relationship."
This I just quoted is a pathological idea that is quite popular these days. Pathological as in "The holder of such a belief will be caused great grief, loss, harm and pain by the belief".
The truth is that trust simply means "I believe X when person Z says X". This belief that you are being told truthful things is not something you can just give away -- it has to be earned through 100% consistency in actions and words across time.
If you feel like you need to check up on what your S.O. is doing, that feeling almost universally stems from an inconsistency that you consciously or subconsciously detected between her stated words and her actions. True emotional intelligence demands that you listen to this feeling of distrust that you have, not that you repress it. Not to mention that by the time you feel a need to snoop, the lack of trust is already there -- it is not a workable solution to deny it and pretend it's not there. And, curiously, 90% of couples in which one of the partners felt the other was cheating, were right. The unconscious mind is said to be 7000 times more potent than the conscious mind -- what the hell are you doing ignoring its very valid computational results?
Now, the poisonous belief I pointed out above is not helpful because instead of helping you deal with what could be a real issue, it only shames you into tolerating it and generates resentment against your partner. This is why the belief is pathological.
Here is the cure for generating boatloads of trust and avoiding every single little temptation that could lead to wrong acts: eliminate the idea of privacy in your relationship through radical honesty. This means no secrets. No secrets about the past. No secrets about your future plans. No secrets about the present, how you are feeling, your conclusions and thoughts. No hiding anything. All questions posed by one of the two will be answered truthfully to the most minute detail possible. No private or secret e-mail accounts or the like. No passwords on phones. No prohibitions on "snooping" (in fact, since you will be voluntarily and reciprocally sharing total and unrequited access to every single method of communication with your S.O., the concept of snooping simply does not apply).
Sure, this is not something you apply two weeks into the relationship, but if you are a couple months together now, this is the absolute best policy. And if you try to put this policy on the table, and your partner takes it off the table, you just know she's hiding something important from you (literally there would be no other rational reason why she would refuse) that you need to know. Ask yourself: do you really want to trust that person that does not trust you?
Why is this the best policy? Well, it simply eliminates any and all possibilities that an emotional affair develop. It eliminates lying. It eliminates cheating or the temptation of inappropriate sharing with others. If your wife / husband is falling for someone, he'll think ten times before using any of these mediums of communication to do it. And that is precisely what you want, because indulging in this guilty pleasure means she / he invests proportionally less time in bonding with you, so you don't want him bonding with someone else.
I concede that most everyone will hate that solution because "everybody's got something to hide" (except for Lennon and his monkey). But I contend that, if you have something to hide to your S.O. that he ought to know or he would want to know, your true self is not in a relationship with them. Do you want to miss out on being loved for what you truly are?