There is no site that is 100 % secure, if you only have a few btc,so you must store it on exchange. Many people are using online wallets, but I don't completely trust online sites and feel better having coins on my desktop. I keep 2 wallets. 1 for online bitcoin wallet for my trading profits and also the another one is hardware wallet which is store most of my bitcoins and just keep it aside.
lol an exchange could run away anytime ,
just like cryptsy that scamming people who store thousands bitcoin there ,
paper wallet is the most secure wallet to store your bitcoin ,
noone can get access to the wallet but you!
That's a common rule of a wallet, I can't say 100% save but almost as long as you do preventive measure correctly.
Different handling according to how much bitcoin you have, if only a little amount, I prefer to save bitcoin in online wallet (but not an exchange) in case I need to do daily transaction but secure your email first and then your wallet with 2fa or anything else.
If you have big amount of bitcoin, offline wallet may the best option to secure it as long as we keep it in a safe place and keep it away from dangerous things.