People still trade baseball cards.There are people at flea markets and a couple of card stores. I'm pretty sure you could find someone to trade with over the internet.
Trading baseball cards (cards of all sporting nature for that matter), is still a hobby done by many, and there are many books, magazines and websites that cater to this group.
People still trade baseball cards. In fact, the business of baseball cards is still quite busy. Older cards are becoming more and more valuable as time progresses and they become more rare.