BoardGameExchange made a splash a year ago as a “new way” to enjoy board games without having to buy them: rent them. There are other places to rent games:

Depending on the rental prices, you may be able to buy games used at nearly the same price as a rental, from places like Half Priced Books or thrift stores; you can get used games online, but shipping tends to add a high percentage to your price. Some stores will let you buy a game and then return it used, or will simply buy your used games, which might also work out to the equivalent of a rental.

You can also borrow game from many libraries (and your friends).