Yes, they can with Wi-Fi. You can't transfer from a Japanese game to English though, or the other way around. Please look around before asking simple questions, by the way. There is a brand new thread in BW that answers a lot of questions like this, and the moderator worked really hard to make it. We do these things to help you, but it won't help you if you don't even look at them or even try to look for them. ;/ And if you were referring to games that were made before Wi-Fi, please ask in the respective Q&A thread. Like I said, they're here for a reason.
Locked.