Users are asking, which receiver we would recommend. The answer depends on many factors amongst application, environment, antenna and price. Focusing on ready-to-use SDR hardware for listening with Windows we can recommend following tested receivers:

Price Model / Manufacturer Frequency Range in MHz Remarkable properties
~ 9 - 15 EUR RTLSDR (DVB-T/DAB with RTL2832+R820T). Search 'RTL2832' or 'R820T' on ebay 24 - 1766 ~ 2.7 MHz bandwidth
For beginners - don't expect wonders!
~ 25 EUR RTLSDR (DVB-T/DAB with RTL2832+R820T2). Search 'R820T2' on ebay 24 - 1766 ~ 2.7 MHz bandwidth
For beginners - don't expect wonders!
Better quality than R820T
Very wide band SDR MK3 / DXpatrol 0.1 - 2000 RTLSDR with switchable HF converter
~ 150 EUR RSP (Radio Spectrum Processor) / SDRplay 0.1 - 2000 Zero IF (I/Q) and Non-Zero IF modes, up to 8 MHz bandwidth
~ 215 EUR FUNcube Dongle Pro+ 0.15 - 240,
420 - 1900
No drivers needed
~ 180 kHz bandwidth
369 EUR FDM-S1 / ELAD 0.02 - 30 ~ 5 MHz bandwidth
Bandpass undersampling up to 200 MHz possible
525 EUR FDM-S2 / ELAD 0.009 - 52,
74 - 108,
135 - 160
~ 5 MHz bandwidth
very good reception quality
Above list is a small selection sorted by price. There are many other recommendable receivers, but we only considered receivers, we have (tested).

For controlling / using a receiver directly from HDSDR you need to install the receiver's ExtIO DLL.
Visit your receiver's website (see below!) and get the appropriate DLL file archive (32Bit [x86] only).
Most sites refer the DLL as "Winrad ExtIO". It will be compatible with HDSDR.
Unpack all files from that archive into the installation directory of HDSDR
f.e. C:\Program Files (x86)\HDSDR\.

Any (monoband) receiver with output to soundcard can be used in HDSDR without any ExtIO DLL.
In this case, HDSDR will not be able to control the LO frequency.

Alinco DJ-X11 + DX-R8 Website
Airspy Download January 08, 2015
Airspy (Alternative ExtIO with more options) Website
Bonito RadioJet 1102S Website
ColibriDDC Website
DiRaWave 0032U Website
Fernempfangsradio Website
Elad FDM-DUOr Website September 12, 2015
Elad FDM-DUO(No HDSDR Transmit capability) Website September 12, 2015
Elad FDM-S1 Website February 26, 2014
Elad FDM-S2 Website September 12, 2014
Elecraft KX3 How-To September 07, 2013
Elektor Website
FUNcube Dongle Base/Pro (FCD) Download December 27, 2012
FUNcube Dongle Pro+ Download August 14, 2014
GenesisRadio G59 Website
Grintek GRX-LAN Website
HackRF One (No Transmit capability) Website
Hamlib v1.5 (for many hardware) Download August 31, 2011
HPSDR (Atlas, Ozy, Mercury) Download January 02, 2013
HPSDR (Hermes) Website April 15, 2014
Microsat easySDR Website
microtelecom PERSEUS DLL   Website
Pappradio Website
PM-SDR Website
QS1R Website
Red Pitaya Website
RFHamFox 1 Website
RFSPACE SDR-IQ / SDR-14 Download April 11, 2013
RTLSDR (DVB-T/DAB with RTL2832) DLL   How-To February 04, 2014
SDR-1 Download April 05, 2012
SDR MK1 / SDR MK1.5 'Andrus' Website
SDRplay Website
Si570 based (Softrock, FA-SDR, FiFi-SDR, Lima-SDR, PM-SDR) Website
Soft66 Website
Softrock Lite v0.12 Download January 06, 2013
USRP, RTLSDR, FUNcube + BorIP network streaming client Website
WiNRADiO WR-G305e' Download May 06, 2013
WiNRADiO WR-G31DDC 'Excalibur' Website

Please report not listed but functional ExtIOs to keep the above list complete.