For both sending & receiving coins you need to connect internet.
What do you mean by "receiving"?
If I have created a wallet and copied the receiving addresses on a piece of paper I don't really need internet connection to receive coins.
I can just give the address to someone and that's it.
Now If I want to spend these coins then I will need internet, but that is sending, no receiving.
You can also spend coins by generating (signing) a transaction on an offline computer, then use a thumbdrive or sd card to move the raw tx to a service that will broadcast that tx to the bitcoin network for you. That way, your private key or brainwallet passphrase need never be revealed to a computer with an internet connection (and its possible collection of installed malware).
There are wallets, such as brainwallet.org that can be run on an offline computer.