Yes, they make goggles that will fit over glasses. I've used them before. I prefer wearing my contacts because glasses don't have anti-fog and you can't push them back up on your nose without removing the goggles, which leads to further fogging...
I would recommend contact, but there are goggles made for glasses. However they will work with regular goggles, just not as well. If u do get regular glasses u can cut a slit in the side foam so that the glasses fit.
Any goggle that's wider than your glasses' frames will work (which are most adult goggles; Soldiers fit a bit tight over my glasses). No need to buy specific OTG goggles. If you're feeling tight then do as other have suggested and cut a small slit in the face foam.
I prefer to wear contacts but I ran out and now i'm stuck wearing my glasses under my goggles. I just got a new pair of goggles that work great though. They're made by S4. I've never heard of the brand before, but my girlfriend got them for $20 on a pro deal cause she's an instructor. They're not designed to go over glasses but the things are huge and damn comfortable and they don't pinch or push my glasses at all. I forget I'm wearing them sometimes. I did some searching and found them for $25 online. There's only two styles from S4, one bubble looking style, and then a more "traditional" style goggle. The least expensive ones (traditional looking) are the ones i have.