I keep Bitcoins in my own computer. I think because the safest. I keep it online but sometimes I find that quite unsafe because I sometimes hear from people that they have been hacked... So that's why I do it on my own PC. 
Its unsafe to save them online but its the easiest way, and the most people choose the easiest way.
I think a paper wallet is the safest option but the problem is that a lot of work.
As said not safe to use online wallets, still blockchain.info seems to be good comparatively. This wallet has the paper code which helps you get your account back even if something goes wrong.