How can I play "The Sims" without an optical drive?
Like most PC/Mac games sold now, The Sims 3 is available for purchase as a digital download. It looks like you can buy it from the official site (note the distinct download and physical options).

Once you purchase it, you’ll be able to download it and install without any physical disks.

It also seems to be available for sale on the Steam online store, also as a download, and as of July 15, 2013, it’s 50% off.