Maybe instead of rarity, could you have it by popularity? Like one way could be based on how many people have it their collection (which isn't necessarily a truly popular game, they might just have it in their collection) or maybe based on a rating system? Like if people rated their favorite games and then while browsing, as well as sorting by alphabetically, you could also sort by popularity? Just a thought. It might be waaaaay too difficult to implement.
Also, is there a feature to add friends? I know you can compare when you look them up, but maybe there could be an option to already have them in a list. Maybe even see what they have added recently?
And this last one is totally just an aesthetic thing. I love the design of the logo. It's so simplistic and clean. I wish there was a picture based clean way to sort your collection and view it.
Overall I'm new and absolutely love this site so far. Sorry if my suggestions are annoying or too much! Can't wait to continue adding my collection on here (1/3 of the way done).