amateur packet radio
In Germany, it is on HF, say, 2m (300 and 1200 BPS), 70cm (1200 to 9600 BPS), 23cm (normally 9600 BPS and up, currently most links between digipeaters) and higher frequencies. There is a KW (short wave) Packet Radio at 300 BPS, too.
Satellites with OSCAR (Orbiting Sattelite Carring Amateur Radio) transponders (mostly attached to commercial satellites by the AMateur SATellite (AMSAT) group) carry Packet Radio mailboxes or digipeaters.
There are both on-line and off-line services on the packet radio network: You can send electronic mail, read bulletins, chat, transfer files, connect to on-line DX-Clusters (DX=far distance) to catch notes typed in by other HAMs about the hottest international KW connections currently coming up (so you can pile up).
There are special "wormholes" all over the world which "tunnel" amateur radio traffic through the Internet to forward mail. Sometimes mails travels over satelites. Normally amateur satellites have strange orbits, however the mail forwarding or mailbox satellites have very predictable orbits. Some wormholes allow HAMs to bridge from Internet to AMPR-NET, e.g. db0fho.ampr.org or db0fho.et-inf.fho-emden.de, but only if you are registered HAM.
Because amateur radio is not for profit, it must not be interconnected to the Internet but it may be connected through the Internet. All people on the (completely free) amateur radio net must be licensed radio amateurs and must have a "call" which is unique all over the world.
There is a special domain AMPR.ORG (44.*.*.*) for amateur radio reserved in the IP space. This domain is split between countries, which can further subdivide it. For example 44.130.*.* is Germany, 44.130.58.* is Augsburg (in Bavaria), and 18.104.22.168 is dg8mgv.ampr.org (you may verify this with nslookup).
Mail transport is only one aspect of packet radio. You can talk interactively (as in chat), read files, or play silly games built in the Packet Radio software. Usually you can use the autorouter to let the digipeater network find a path to the station you want. However there are many (sometimes software incompatible) digipeaters out there, which the router cannot use. Paths over 1000 km are unlikely to be useable for real-time communication and long paths can introduce significant delay times (answer latency).