Lots of choices here but they generally fall into the two categories of communications receivers/ scanners and software defined radio (SDR). In the first category, these receivers tend to operate up to several hundred megahertz and are usually reasonably sensitive. If you have an old shortwave receiver, first dust off the spiders, connect it to your new 15 metre band dipole array and you should receive the Sun or even Jupiter if you're lucky. The quality HF communications receivers used by ham radio enthusiasts are a good option, there is quite a lot of software support for the Icom IC-7000 Series and if you look hard enough, quite a few others as well. There are also many ARRL members and enthusiasts developing their own radio hardware which are often better than many commercial models.
Some links you might find helpful are: Rick Campbel KK7B & Bill Kelsey N8ET R1/R2 & Mini R2 Pro Direct Conversion Receiver QPL2000 Project
SDR is the new toy of choice in the radio world. There are many models appearing not only in the HF and amateur radio bands but wideband models as well operating well into the gigahertz ranges.
There are also many ARRL members and enthusiasts developing their own SDR hardware.
Some of the more popular models are listed below along with links to their respective websites:
Universal Radio SDR-14 & SDR-IQ
Ten-Tec RX-331 SDR (Our page) and Ten-Tec RX-331 SDR (OEM page)
Ettus Research USRP and the new USRP2
WinRadio G305e (Our page) and WinRadio G305 and G315 Series (OEM page)