The prototypical board game bookshelf is still from Ikea, the KALLAX. They've got the deep square shelves that can hold six or seven square box board games pretty easily. If you look at almost any board game reviewers, behind them is nothing but Kallax shelves (especially Dice Tower).

I've got 1 2x4 and 2 2x2s and they hold about 90 games total. On the 2x2s I have about 10 of the small box (Kosmos sized) 2 player games and on the other I have 2 baskets for tiny card games that holds about 30 more games). I also keep some games on top of my 2x4 Kallax. So they probably hold about 125 games total.

Too bad I own about 200 games. :/