You will hear both, but 'by' is more common and sounds a little better to my ears. We tend to use 'by' rather than 'at' when referring to people.

"By" would be the better choice. With "by" you would be stating something like the following. Brackets indicate implied words. I’d never seen so many people before. I was amazed by [the attendance of the people in] the crowds. With "at" you would be stating something like the following. Brackets indicate implied words. I’d never seen so many people before. I was amazed at [the attitude of the people in] the crowds. If you were talking about a one-time event, you may want to consider using crowd instead of crowds. If you used crowds, you are suggesting you saw more than one group of people.