The iPhone has an UMTS radio that supports the following bands: 850, 900, 1900, 2100 MHz. For GSM/EDGE it supports the 850, 900, 1800, and 1900 MHz bands.

http://www.apple.com/iphone/specs.html

In the US, AT&T uses the 850 and 1900 Mhz bands. (There's no other network in the US that has iPhone-compatible 3G service.)

In Australia, Telstra uses the 850 Mhz band, others use the 2100 Mhz band.

In Japan, 1700 and 2100 Mhz bands are used.

All of these frequencies, except for the 1700 Mhz band, are supported by the iPhone 4.

http://www.worldtimezone.com/gsm.html

As far as I can tell, there is only a single quad-band GSM + quad-band 3G/UMTS version of the iPhone; there don't seem to be any regional differences in the hardware. So as long as your target network supports a subset of those bands, you should be fine. In the US, CDMA networks won't work (Verizon, maybe others?), and in Japan you'll be limited to 3G as there's no GSM. Australia, like Europe, uses 900/1800MHz GSM, so you'll be fine.