List of sites with free HDRi
There are links to various HDRIs scattered all over the Iray threads...well, HDRIs aren't just for Iray. 3Delight, Luxrender, Cycles and Octane all can use them too. Some are in spherical mapping, most are equirectangular/latitudinal-longitudinal mappings...a few are in both, very few are cubic.
Wide quality range
The quality of these will vary greatly, many require a supplemental light source (usually in the location of the sun) to cast 'hard shadows'...most are non-comm only. (Non-comm = Non-commercial use only, but read the individual licenses on each site/item to be sure.)
Mid to High dynamic range
Most of these are mid to very high range, most will cast decent shadows. Many/most of these will cast 'hard' shadows without any additional light sources. Quality and license, noted; ones without comment are either no restrictions or unknown. Many of these sites also have pay versions that range from fairly cheap to rather expensive...but licensing is usually much more 'commercial' friendly for the paid versions and there are either higher range HDRs/higher res backplates with the paid ones.
http://www.aversis.be/hdri/ (monthly freebie, non-comm only) *
http://hdrmaps.com/freebies (several free ones, some are usable in commercial renders) *
http://www.dylansisson.com/project/panoramas/ (non-comm) *
http://www.doschdesign.com/samples.php (possibly commercial use) *
http://www.dutch360hdr.com/shop/ (varies...more than at the sIBL archive site) *
http://www.hdrmill.com/Freebies.htm (these are low to midrange) *
http://www.openfootage.net/?cat=212 (varies..quality and license...the pay for ones are very good..and pretty cheap. He also always has a render with the image that shows the shadows cast by the image) *
https://www.moofe.com/#/free (somewhat convoluted and restrictive Terms)
http://gl.ict.usc.edu/Data/HighResProbes/ (of course, the 'granddaddy' of HDRI resources) *
http://www.pauldebevec.com/Probes/ (basically the same as above, but also cubic maps...and possibly lower resolution)
http://www.turbosquid.com/FullPreview/Index.cfm?ID=925039&seo=0 (may be more on Turbosquid...)
http://www.food4rhino.com/browse?searchterm=brianjames+hdr (mostly seem to be non-comm)
http://www.zwischendrin.com/en/browse/hdri (no sort function I could find, the free ones are scattered throughout the pages)
http://www.viz-people.com/portfolio/free-hdri-maps/ (non-comm and registration required)
http://bocostudio.com/boco-pano/ (use in commercial renders allowed)
http://joostvanhoutte.com/hdris/ (pack of 26 images, most are able to be used commercially)
http://www.whitemagus3dmodels.com (use in commercial renders allowed, mostly large sky images)
http://giantcowfilms.com/2015/11/23/hdr-morning-sun-winter (some of these are listed as CC0 and the stops are listed: 20+)
Low to mid dynamic range
Some with very nice shadows, many spherical only
http://dativ.at/lightprobes/ (Non-comm) *
http://www.maximeroz.com/hdri-free-pack (this is interiors...)
http://www.unparent.com/photos_probes.html (Brycers may be familiar with these)
http://sith-kitten.deviantart.com/art/Iray-Skies-Volume-1-522179745 (There are 3 hdrs, some backplates and a set of sample renders. All designed with Studio and Iray in mind.)
These are ones I know that are just low range, backdrop or skies only...
http://blenderartists.org/forum/showthread.php?24038-Free-high-res-skymaps-(Massive-07-update!) (no restrictions, just sky maps)
http://www.evermotion.org/tutorials/show/7928/free-hdri-cd-collection-from-evermotion (variable quality, mostly just skies) *
http://shtlab.blogspot.com/2009/08/hdri-panoramic-skies-for-free.html (usable for lighting, created in Vue)
https://www.hdripanorama.com/free-hdri-skies (low to mid, 'purchase' required)
http://www.cgskies.com/ (free ones are low to mid, high are for sale)
http://hdri-skies.com/ (4k sky images, commercial renders allowed)
http://texturify.com/ (a number of nice LDR panos, suitible for backdrops)
And these are nice for 'studio' shots...
http://zbyg.deviantart.com/art/Free-HDR-For-Studio-Render-157557355 (hi-res) *
These have been made by steveathome, specifically for Studio and Iray (work in Luxrender and 3Delight, too...don't have the Octane plugin, so I haven't tried any of them there)
Forum thread: http://www.daz3d.com/forums/discussion/58153/
A new set by valzheimer...
Forum thread: http://www.daz3d.com/forums/discussion/129346/free-rgb-hdri-soft-lights-for-iray-by-valzheimer#latest Lights: http://www.valzheimer.info/2016/11/va2016-rgb-hdri-soft-lights-for-daz.html (79MB)
* ones I've actually used and have had very good results with...the others I haven't used.
I thought about it. Since this is a freebie HDR thread, here's some utilities to go with the images.
http://hugin.sourceforge.net/download/ (this is a panorama 'stitcher' to assemble nice 360 images)
Another source, sometimes even for full versions of some of the high end/price pay-for HDRis...magazines. The included disks/content downloads for many of the computer graphics magazines have offered HDRis at various times. Very often, these are in the high to very high dynamic range categories.
http://adaptivesamples.com/2013/11/17/how-to-create-your-own-hdr-environment-images/ (fairly good tutorial on creating HDR maps)
Tweaking in Photoshop: http://hdrmaps.com/blog/tweaking-hdri-in-photoshop/ (thanks Arnold)
HDRI Setup in Modo: http://www.hdrishop.com/pages/tutorials (basics are the same for any renderer)
How to Create a Custom Studio HDR Map: http://cgalter.com/custom-studio-hdr/ (As posted by Laurie in this thread http://www.daz3d.com/forums/discussion/127241/hdr-fun#latest)
And I'm sure I'm missing some...