Most people don't store ALL of their money in one place.
As an example, I have some USD.
Some of my USD is stored in an account at the bank.
This USD is not always convenient to access. I have to go to the bank (or an ATM) to get it. The bank is only open certain hours, on certain days. There can be fees at times when attempting to access the USD. While this is the least convenient of the three storages, it is protected by multiple significant and expensive security measures and is insured against loss and theft by the F.D.I.C.
Some of my USD is stored in a safe in my house.
This USD is much more convenient to access. I can get some of it whenever I am at home. It isn't as well insured, and the security measures aren't quite as extensive as the bank's, but it is generally safe most of the time. I wouldn't want to keep my "life savings" in there, but I store more there than I would typically spend in a given day.
Some of my USD is stored in my wallet in my back pocket.
This is extremely convenient to access. I always have it with me, and can just pull some out whenever I want to spend it. It isn't insured at all, and can easily be lost to a pick-pocket or a mugger. I can become distracted and accidentally leave it somewhere, losing it. I have enough in there for most anything I might want to buy on a typical day, and I re-fill it from the safe in my house when necessary. While I'd be frustrated if I lost everything in the wallet, it wouldn't be devastating.
You can do something similar with your bitcoins.
Store most of your bitcoins in offline storage (such as Paper wallets). It will be inconvenient to access, but it will be the most secure sotrage you have.
Store some of your bitcoins in an internet connected desktop wallet protected with encryption (something like Electrum, MultiBit, or Bitcoin Core). These are more convenient to access than a paper wallet, but are also more susceptible to threats such as keystroke loggers, hackers, and malware. They are also difficult to use when you are not at home.
Finally, use a web hosted wallet (such as blockchain.info) to store enough for most anything you might want to buy on a typical day. You can re-fill it from your desktop wallet at home when necessary. Don't store an amount there that would be devastating to lose.
+1 on this. I don't think however it is possible to have quite as many levels of protection/convenience for storing your bitcoin. All you can really have is a hot wallet/storage and a cold wallet/storage. I guess you could store some bitcoin on a wallet on your phone that might be considered to be more "hot" then bitcoin stored on your "online" computer however it would really not be that much less secure