From how far can radios receive a signal?

It depends on six factors:

1. Transmitter power,

2. Transmitting antenna,

3. Receiving antenna,

4. Receiver sensitivity,

5. Frequency and type of operation,

6. Any land or obstacles between the two radiOS.

The deep space probe that passed by jupiter, neptune and the outer planets was still sending from billions of kilometres away.

A small iPod FM transmitter, such as the ones used to broadcast fro an iPod to a car radio have a range of less than ten metres.

2.4 GHz Wi-Wi can have a range as small as one room (depending on building construction) or hundreds of kilometres with large antennas sited on mountain tops.

Generally? Don't believe sales hype - ask somebody who uses similar equipment, or ask to test the gear yourself under the conditions you expect to use it in.

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Another contributor provided a benchmark:

As of December 2010, the Voyager I spacecraft, launched by NASA in September 1977,

is still operating, and communicating with earth by radio, from its position on the 'edge'

of interstellar space, presently about 10.6 billion miles from us.