I use both.
When I've downloaded something I don't burn it to a disc or whatever, I just keep the digital file. But when I actually buy something, I want the physical product.
I don't trust companies to keep my files forever. If I purchased a Blizzard or Steam product and they go bankrupt in the future (unlikely, but just an example) I will not be able to access the game I bought. I can also keep a backup on my computer, but what if it crashes?
By the way, this is also the reason I really hate all sorts of online protection in games. What if the company doesn't exist in the future? You won't be able to install your game, since the protection required you to access their servers.
No, I'd rather keep a physical copy. Though it can also be damaged or lost, the chances of the happening are smaller imo.