What is the maximum range of radios operated by amateurs?

And what are the usual activities of radio amateurs?

(Or which people do they communicate with?)

Other answer:

Tempting Apple:
Anywhere in the world. Personally, I stayed mostly on 40 meters with power of 100W or under and a dipole antenna so for me 1000 miles was a distant contact!

Activities vary widely. Some hams are interested in the technical side of it (me) and some like just getting on the air and chewing the fat. Contests are popular, and I always liked "field day" contests where hams would set up their rigs with batteries or generators and log contacts like crazy for 24 hours.

In the worst disasters hams are an important contact with the outside world during the first desperate hours.

Check out the ARRL (source) for more. You will meet a lot of great people at ham activities. Age is not a barrier (I was 15 when I got my novice license).

Small Business Owner in TX:
Amplitude Modulated signals (AM radio, for example) are at low frequencies and therefore have long wavelengths. These can bounce off the ionosphere and literally can sometimes, with ideal weather conditions, travel thousands of miles, with good clarity. Winter seems best, at night. l used to listen to an AM station in Lima Peru (broadcasting in English) while I was in Arizona.
cato___:
Some Amateur Radio Operators communicate with each other by bouncing signals off the moon. I think that's 1,250,000 miles each way….so …about 2,500,000 miles round trip. Not surprisingly, this mode of operation is called moon bounce. I'm sure you can google it
Sailor:
It depends on the radio frequency. VHF and UHF line of sight between the aerials. MF up to 600 miles and HF thousands of miles.
fuzzy:
depending on rig power, aerial, frequency, time of day, ionospheric conditions, operator skill anywhere around the world