I use paper wallets to store my bitcoins... i have around 7 -10 wallets now, I use multiple just to make sure the others are safe when one wallet is hacked. I don't have much coins though, but that's the safest way i could think of right now to keep them safe.
Having too many paper wallets might pose an
operational risk. The risk is that you might lose some of them or even forget about those that have too few BTC. If your private key generation method is solid there is really no point in having more keys than necessary. On the other hand if you generate private keys using a silly method (like using quotes Shakespeare) then all your keys are susceptible to hacking no matter how many you have.