Okay, my backstory is this:

My current boyfriend is amazing. Wonderful, loving, funny, all that good stuff. He is from a city about 4 hours from mine, and we met while I was on a trip and it was love at first sight for both of us. Eventually things became serious and we both moved to a new city together, for the sake of adventure and our relationship. Everything has been amazing and wonderful since we moved in together, I'm happy, he's happy, were in love.

The trouble is this:

I just found out through friends that he was sleeping with A LOT of other women during the time that we were still living apart. I know we weren't sure how serious our relationship would be, and half the time if we would even see each other again! We didn't have established rules, or even talk about our relationship until much farther down the road, but it's really bugging me lately! After I met him I didn't want to be with anyone else! I couldn't imagine it! So my problem: How can I get over this? I know it shouldn't bother me but it does. He's such a great guy, I am shocked to find this out, and am not happy about it. But I can't really say anything, can I?

found out through friends that he was sleeping with A LOT of other women during the time that we were still living apart.
Why be shocked and screw up a relationship over the sayings of others. Best to start now, and move forward.

But I can't really say anything, can I?
Nor should you, but don't wear blinders, and see what happens. As you say, things were up in the air before, and you only have the word of others as to what he did. Not enough to go on in my opinion

I agree with Tal,

Yes, it probably stings to know that he was sleeping with lots of girls when you weren't official, it would bother me too, but there's not a dang thing you can do about it. That was past and you're together now, and he better not be doing that now! You can talk to him, but it's really not going to do much good, he's just going to get uncomfortable and it won't solve anything. Just know that you are the lucky one that snagged him, not those other girls.. You're probably (making an assumption here) going to marry the guy and grow old with him and you won't ever have to worry about him doing that again... so lick your wounds and move on.. you're happy in the relationship, revel in that!

I agree with what Tal said about listening to others. Beyond that, I want to point out this guy moved 4 hours from his location for you. I think he likes you.

Don't be one of "those" girls. Those girls take a wonderful guy and if they can't find real sins to laud over them, they create scenarios of wrong-doing for which the guy can never ever win.

I just found out through friends...
Stop taking gossip from friends into your most intimate relationship.

...that he was sleeping with A LOT of other women during the time that we were still living apart.
So you weren't officially together, but he should've known better? Right? Wrong. That's only what "those girls" say.

I know we weren't sure how serious our relationship would be, and half the time if we would even see each other again!
Ah, see, you admit there was clearly no commitment, but you're laying the groundwork to be mad anyway? Tsk, tsk.

We didn't have established rules, or even talk about our relationship until much farther down the road, but it's really bugging me lately!
BING-BING-BING - "those girls" have officially entered the building. You DO know how unfair all this is, right? Not just to him, but to yourself as well.

After I met him I didn't want to be with anyone else! I couldn't imagine it!
And imagine how it would've been if you two had discussed THAT and made it a reality instead of what you DID do? Oh well, you going to punish HIM for what you wish you'd done differently? I know how "those girls" would answer that, how about you?

How can I get over this? I know it shouldn't bother me but it does.
Wow, you're covering all the bases here. You admit he hasn't done anything wrong, and then dive right back into "but I'm going to be mad about it anyway."

He's such a great guy
Prove it. Treat him like a great guy.

I am shocked to find this out, and am not happy about it.
Shocked why? Seriously, why! This issue is non-existent. It's a mental hurdle you have created all on your own based on rules that didn't exist, a relationship that wasn't (yet) and you're now gearing up to dole out punishment and speeches to him as if there were ANYTHING he could do/say to make it better. This is the worst possible kind of behavior to bestow on someone you claim to be "crazy" about.

But I can't really say anything, can I?
BING BING BING BING!! Moreover, you not only don't say anything, you slap yourself silly every time you detect this kind of thinking.

What you're doing here will only accomplish two things:
1) The guy you like will smartly run screaming in the other direction
2) He'll stay and take the abuse from you, and you two will have a wonderfully unhealthy relationship (but at least you'll have the upper hand)

You lose either way. Act lovingly. Think lovingly. Respond lovingly. Tolerate everything you can but only the REAL stuff. The made up stuff (like this) you completely ignore.

Good luck, dearie.