GHz receiving isn't usually practical for casual listening... it typically involves hunting for signals with tuned directional antennas, and the signals are often digitally modulated. But some people enjoy experimenting and trying to decode the digital, or just tracking satellites by receiving the signals or CW beacons.
As Jeroen3 said, you can get a general sense for what is up there by looking at a frequency allocation table from your country (or the ITU). You may also be able to find a list of specific frequencies used in your area, since most likely anything you hear on UHF (300 Mhz+) is going to either be a local station or a satellite.
The top end of the UHF band is 3 GHz, so a typical wide-band receiver IC is probably designed to operate up to there. If the circuit supports it, there isn't really a reason for a receiver manufacturer to artificially limit the coverage of the receiver. In other words, they aren't adding additional circuitry to receive GHz because there is useful demand for it, it just so happens that the chips used already support it.