Does there exist an internet-like peer-to-peer packet radio system?

units will connect automatically to nearest units of same system, and generate a routing table, and therefore you can send your message anywhere in the network, so that other units will relay your message forward until it reaches its destination.

What you are describing is a mesh network, or more specifically a wireless mesh network. So the short answer is yes, someone has done it already.

As others have pointed out, radio amateurs implemented this over 20 years ago in a system known as APRS. To use APRS on the amateur bands require one to be a licensed radio amateur however.

In the commercial space there are many companies offering mesh network devices such as Ruckus and Village Telco with their mesh potato for voice in the third world. Another vendor of low cost devices is Open Mesh.

For amateur radio, the latest incarnation for high speed mesh networking is HSMM-MESH -

HSMM-MESH™ is a high speed, self discovering, self configuring, fault tolerant, wireless computer network that can run for days from a fully charged car battery, or indefinitely with the addition of a modest solar array or other supplemental power source. The focus is on emergency communications.

In its current form it is built using the Linksys WRT54GL wireless router and operates on channels 1-6 of the 2.4GHz ISM band, which overlaps with the upper portion of the 13cm amateur radio band. Other platforms and bands may be supported as development resources permit.

I don't think X.25 is relevant here.

AFAIK various bands that are legal for speach are not legal for digital transmission. Check with a HAM specialist.

What you want is essentially an IP network with totally dynamic routing (the destination address holds no information about the location of the desination). In a non-radio (or directional radio) situation the problem is how each node should route its packets. It must basically have a routing map that has, for each destination, a direction (next hop) to send the packet to. This can be done, but the memory requirement in each node is linear in the number of nodes.

In a non-directional radio situation things get much more interesting. The question is not to which node a packet should be forwarded, but whether a station should re-broadcast a packet at all. That requires both knowledge of the direction in which the destination lies (compared to the previous sender and my own loaction), and knowledge of whether this particular packet has already been (re) transmitted recently. Interesting problem. An airtime-efficient solution requires a lot of memory.

Note that maintaining dynamic routing information is a hairy problem in itself. Think of the good-news-travels-fast but bad-news-dies-slowly problem. And how robuust should the system be against a single malfunctioning (or even malicious!) node?

A very simple (and robuust) implementation would 'flood' each packet through the entire network. This reduces the bandwith drastically, especially when stations are close compared to their range.