One of my favorites was Green Tiger Press, which sold (sells) artsy children's books and interesting cards and prints, often based on vintage images such as the one below (available in the greeting card and also in the art print categories).
These days I do most of my specialty (for things I can't buy locally) shopping online, although I still receive catalogs. Many online shops send buyers paper catalogs once you've ordered from them, so year round and especially at Christmas catalogs arrive in my mailbox. I enjoy looking at them, although I confess to feeling a bit guilty about all that paper being used when I can easily go online to shop (I get it, though. It's easy to forget that a store exists if you don't get a nudge now and then. Paper catalogs are gentle nudges. And they work). If you're interested in finding places that still send out catalogs, do a search of "fashion catalogs," "clothing catalogs," "children's toy catalogs," "mail order book catalogs," or whatever category strikes your fancy. You can also find some (not nearly all) catalogs via catalogs.com. If you're not sure if an online store has a paper catalog, scroll to the bottom of the page. You'll often find a "request a catalog" link there.
What catalogs do you still receive?
Have a great day!