Is there a way to tag games you have not purchased yet, maybe to tag some games as high/low priority purchases?

Tagging is limited only to purchased games in your account, but you could create a GOGmix for the games you are interested in.

A good example of what Grargar mentions can be seen here, with notes regarding high and low priority by the list creator: http://www.gog.com/mix/tannaths_wishlist

Or you could simply add the ones you want to purchase to your wishlist.

One of the things I'd like to do is mark unpurchased games that I have looked at and was not interested in so I don't have to check them again to see if I would like to buy them.

That wouldn't be bad. I'd like to be able to tag the ones I own already outside GOG.

I've created a wishlist for that:
http://www.gog.com/wishlist/site/add_tags_for_unpurchased_games

Lol, I was wondering why it got 3 more votes since last night. :)

I have already left some feedback somewhere regarding the new account suggesting they add tags to the wishlist as well, don't know if GOG staff read it or are willing to do it.