Not a typical Japanese pun, I suppose, but a pun story I heard:

There was a Korean guy working in a Japanese company.

One day, his coworker went out to the roof for a quick cigarette break. Another person came in and asked where he was, so the Korean guy would reply (in Japanese), "Oh, Mr. Tanaka is taking a break, on top of the roof."

The person blushes, and leaves wordlessly. The Korean guy is confused, and then realizes he used the Korean word for the roof: "oksang".

(Japanese okusan = wife)