Email is what they call a "store and forward" technology. You don't have to be online to receive it.
The problem is with the forward part: it doesn't. You have to go get it. This is what they call "polling". Computer scientists usually discourage polling because it's a waste of resources; constantly going out and looking for things that might be happening. A better mechanism is notification. Operating systems use notifications, deep down inside their inner workings. Cell phones do this. Telephones do this: your phone does not touch base with the central office every 5 seconds to see if there are any incoming phone calls.
Email used to actually use forwarding, back in the days of UUCP (which stands for Unix-to-Unix-CoPy). Usenet is still (mostly) store-and-forward. A system would dial another system on the modem when there was mail to be delivered. It worked great.
Nowadays POP and IMAP protocols use polling (Check New Mail...), and web mail uses an even more primitive form of polling: human beings, who need to actually browse their way to a web site.
This is becoming more and more important (despite the spam epidemic) as people manage their online and offline states, use IM software, travel across time zones, etc. The question of whether or not "you have new mail" has become an obsessive cultural diversion.
If this issue interests you, check out our software, InterComm. We use groups, and people communicate with sets of people, online or not. Messages are actually stored in the group, and they're actually forwarded to you if you're not onlinethrough email, yes, or through text messaging on your phone or handheld, which truly is a forwarding technology. It's refreshing, and amazing, at the same time.