What are the most popular board games/ family games in Japan?

Question:

Also, do Japanese play "carrom board"?

Answer:

Japanese kids these days play computer games and psp, but 囲碁 (igo)、将棋 (shougi)、麻雀 (mah-jong) are still popular. We still have 囲碁-only channel on tv that's talking about 囲碁 strategies all day. My grandpa used to watch it every day. University students pull an all-nighter playing 麻雀 (that's a traditional student culture). Some prefer Chess (western将棋) but I think it's less popular. 人生ゲーム is also famous but I've never played it before.

I don't know about the carrom board. But some people seem to play carrom board.

Japan Carrom Federation
http://www.carromjapan.com/