I know that now a days you can download games on to the console. I believe what ever it is you download is supposed to be saved in some type of cloud so if you play on a different console your purchased games arw still there.Though I still like having a physical copy. For some people, they like renting games which I believe a company called dragon fly does.
I usually prefer buying physical games. Being able to resell them or trade them in if I didn't enjoy it is always a plus. I only buy digital if they are classic games that I can't get anywhere else.
I used to be a hardcore physical buyer, but I'm straying ever closer to digital-only these days. It's much more convenient. That said, it really depends on the game. If it's an expensive title (your Metal Gear Solids and Dragon Ages and so forth) I'll more often go physical. Smaller games... eh. Digital is fine. So many indie titles on Steam are digital only, so in many cases the decision is made for me regardless.
I prefer buying physical games as well even though digital downloads are cheaper upfront. I have a group of friends that I trade games with so I can usually get to play multiple new titles if I had one or two sought after titles that my friends would be happy to trade me for. Without this, however, I don't think I'd be too interested in buying physical copies since I'd have to resort to selling my old games through resellers or sell it myself through online markets which I'm not too keen on doing because it's much more trouble than I'm willing to put up with for video games.
On console, I find that physical copies of games are usually way cheaper than what, say, the Xbox Live store offers. Gamefly has under $20 blow out sales for physical copies of games. Another plus for physical copies is that its easy to resell or lend them. I also have a gaming computer, and almost none of my games for it are physical. And even the physical copies came with online codes. Simply put, physical copies are cheaper for console, but more costly for PC.
Game Fly also does renting games as well. I always wait until they're cheaper at the store until I buy a game. I can't justify spending $60 for a brand new game when I could just wait, and also see what other people are saying about it too before I get it and play. And someone made a great point that you can resell them if you keep them in good condition. I'm more interested in physical copies if they're something I'm looking forward to and is a popular game, but for those not that big I could do a digital.