If I wanted to print my bitcoins? Suppose I wanted to print my bitcoins to paper for safekeeping.  It would be impossible for a hacker to get at my computer.  To do so I need to know where to find the private keys.  Is there only one private key and many public keys?   Does it make sense to carry a printed bitcoin in my pocket and type it in someplace else?  Your thoughts on this matter, please.
There are many pairs of private-public keys. The usual wallet.dat starts with 100 keypairs, although usually you use only a few. To get your keys you can use Pywallet. Then you can print them as they are, or as QR codes.

You should note however, you are not printing Bitcoins, but the keys you use to get to them. This is more like printing username and password to your paypal account, rather than printing money.

Carrying your printed keys is only useful if you intend on paying with them (and only as much as you need in case you loose your printed key). As not many people accept Bitcoins nowadays, it is not too useful.