What type of a private wallet do you use? Is it offline, cloud service?
So this is sort of a loaded question.
There are several different ways you can go. There are 4ish types of wallets that you can use, and they have their tradeoffs. The first is the default wallet that is provided by the devs of the currency that you are using. Second there are the exchange wallet services, both the online wallets like CoinBase has that are connected to the internet and allow for instant trading and transfer. There are also the cold storage wallets like CoinBase's vault service. The wallet is disconnected from the internet and takes several days to move funds based on the policy of the provider(because the wallets need to be retrieved, connected to the internet, verified, etc).
The third kind of wallet is a paper wallet(or app wallet). This is a wallet that uses SPV(Simplified Payment Verification). A portion of the blockchain is stored on your device and is connected to the network. The fourth kind is a hardware wallet, which is what Phil was talking about earlier. This is a physical device that is considered cold storage because it is disconnected from the internet.
Of the 4 wallets that I described 3 of them allow you to keep your private keys. The exchange wallets are kept by that particular exchange. I've talked about it in here or you can google Mt Gox, but they are the reason you don't want to keep your coins on exchanges for extended periods of time.
Now to your original question. I use a combination of default and paper wallets. The particulars I won't get into but you can generate as many addresses as you want, which are all completely independent of each other. I keep the pass phrases for these wallets in a number of safe locations. I also have my coins spread out over different wallets to minimize risk of compromising a single wallet with everything in it.
It really just depends how and where you want to keep your assets.
