I'm not aware of any team other than the Yomiuri Giants giving away free cards at the stadium, and they've been doing it for quite some time. Other teams do have cards, but those are almost exclusively distributed through their fan clubs.
I came across a bunch of "Players Card" singles a few months ago. I found so many, in fact, that I'm splitting this up across two posts. Here is the first stack, from April through July 2013. The card front design remained fairly consistent, but there are some different back styles, as you can see below. The variations occur on the two dual-player cards, using somewhat different designs to provide all of the information for each player on their "front" side.