Software Defined Radio experimentation has been getting cheaper with the advent of front ends such as the FunCube dongle ($175) or the Softrock SDR ($70, kit). An even more compelling solution are SDRs using Realtek RTL2832U/Elonics E4000 based USB DVB-T tuners. USB DVB-T tuners are used to receive digital TV broacasts in Europe, but with the right drivers and software, can be repurposed to receive radio signals in the 64Mhz to 1.7 Ghz range. With an appropriate downconverter, DC to 50Mhz is also possible. Best of all, DVB-T dongles are cheap (less than $30), widely available (the SDRs mentioned above are frequently out of stock) and ready to use out of the box (no soldering required, unlike the Softrock).
I use the Ezcap 666 USB 2.0 DVB-T/DAB/FM dongle, procured from Ebay, specifically from seller 'noelec' who has sold more than 250 of them for $27.75 including shipping.
Although the unit comes with a small antenna, you may prefer something more robust, as even a "rabbit ears" TV antenna will result in better reception. To do this, you will need a "European TV adapter", Radio shack part number 278-261 (shown on the right attached to the dongle), as well as a TV antenna. If you would rather connect your Jpole of VHF/UHF beam, look for a MCX DVB to SMA adapter. In my experience, with the stock antenna, you will hear a lot of strong public service stations and some strong repeaters. A cheap rabbit ears antenna is enough to pick up most local repeaters.
Finally, you will need a sufficiently powerful PC to connect the dongle to. I use an Intel i7 based laptop, and the software described below uses less than 10% of CPU. I have heard of some people having success with netbooks, I guess it just depends on whether you want to use your PC for anything else while listening.
Software is available for Windows, Mac and Linux. In this post, I concentrate on Windows, although I may cover Mac installation in a future post.
You will not need the drivers (if any) that ship with the dongle. Instead you will need a program called Zadig, a Windows installer for USB device drivers. You will also need an SDR program, such as WinSDR, HDSDR or SDR#. I highly recommend SDR#, for its ease of installation and the availability of source code in C#, something I have already put to good use by adding a frequency manager and scanning functionality. Detailed installation instructions are available here, and will result in a working system, ready for hours of fun.