I've never had a problem with my regular glasses on those rides. My bad luck is with sunglasses. I've lost two pairs so far, but not as a result of the rides themselves. The first was while unloading at Grand Fiesta Tour. My mom had left her purse on the boat seat and when I bent down to pick it up, my sunglasses fell off the collar of my shirt and right into the water. The second was while exploring Tom Sawyer's Island.
I usually make sure they're snug, but I never take them off. If they're loose, I'd suggest putting them in a glasses case in a pocket or bag so they don't break.
I usually wear contacts, but if I wear a lanyard I take it off and either hold it, or put it away. Or I hold it down while I ride. I haven't been to a park with my glasses in years. As for sunglasses, I put them away or put them on my shirt. Your best bet is to put them away to not take any chances.
I always wear my contacts. I can't stand my glasses sliding on my nose due to sweat or taking a chance of losing them on the ride. If not contacts I'd just take them off. If I take mine off I can't see much and I hate that