People regularly ask about where to buy CD quality or hi-res downloads (legitimately!) so here is a list of sites I know of. Please post a comment if there are any I've missed. Note that they must have music available in a lossless or high-res format available.

2019: Please note that MQA is NOT lossless, so it wont be included here.

Format guide:
  1. CD Quality = 16 bit, 44.1 kHz PCM.
  2. Hi-res = Any of 24 bit; 44.1, 48, 88.2, 96, 176.4 or 192 kHz PCM.
  3. DSD = Direct Stream Digital ie: SACD-type files that requires special playback software that can convert the files to PCM on playback or a DAC that can receive the DSD data unchanged. DSD64 = 2.8 MHz. Dual-rate DSD = DSD128 = 5.6 MHz. Quad-rate DSD = DSD256 = 11.2 Mhz.
  4. DXD = Digital eXtreme Definition - 24 bit 352.8 kHz PCM. Requires a DAC that can receive and decode 384 kHz PCM over USB. Usually only used in recording music that will be distributed as both DSD and Hi-res.
  5. 5.1 = Dolby Surround Sound multi-channel.

Commercial sites:

Acousense
Genres:
Formats: Hi-res
Notes: Site only sells physical media (including hi-res files). See Linn Records or HIGHRESAUDIO for their download catalogue.

bandcamp.com
Genres: wide variety of self-publishing musicians
Formats: Bandcamp.com supports almost all digital formats, ranging from CD-quality and hi-res lossless FLAC, ALAC, WAV, and AIFF to lossy MP3, OGG, and WMA. Limitations may depend on the particular artist selling through the site.

Blue Coast Records
Genres:
Formats:
CD Quality, Hi-res, DSD
Notes: Sister site of Downloads Now!

Bowers & Wilkins Society of Sound
Genres: Classical, Rock, Pop.
Formats: Hi-res, CD Quality
Notes: Subscription service offers 2 albums a month. Product registrants get 3 months free. Trial available.

Cardas
Genres
: Jazz, vocals and others.
Formats: Hi-res
Notes: Most are on CDs or thumb drives with a handful of downloads.

Cedille Records
Genres: Classical, Vocals, contemporary.
Formats: CD Quality, Hi-res.
Notes: CD Quality only available as MP3.

Downloads NOW!
Genres: Various
Formats: CD Quality, Hi-res, DSD
Notes: Consists of a number of "micro stores" from various artists.

e-onkyo music
Genres
: Pop, Rock, Classical, Jazz, J-Pop
Formats: Hi-res, DSD, DXD
Notes: Japanese language-only site. May not sell outside of Japan geo-identified IP addresses. Nice selection of 192/24 hi-res rock and pop titles not yet available in the US.

Flacme.com
Genres: various
Formats: CD Quality, Hi-res
This is a search engine that will point you at a source of hi-res downloads if available

gubemusic.com
Genres: eclectic
Formats: CD Quality, Hi-res

Hifitrack
Genres: Asian artists mostly.
Formats: CD Quality, Hi-res.

High Definition Tape Transfers
Genres: Classical, Vocal.
Formats: Hi-res, HQCD (High Quality CD physical media), DSD, DXD.

Hi-Res Music
Genres: Various
Formats: DVD-A remasters (physical media only).

HIGHRESAUDIO
Genres: Not listed.
Formats: CD Quality, Hi-res, DSD.
Notes: Hi-res up to DXD. May not work in all countries.

HDTracks
Genres: Blues, Country & Bluegrass, R&B, Gospel & Religious, Classical, Pop, Electronic, New Age, Soundtrack, Historical, Industrial, Contemporary Cristian, World, Rock, Jazz, Holiday, Latin, Reggae, Hip Hop/Rap, Folk, Children's, Indie, Fusion and others.
Formats: CD Quality, Hi-res.
Notes: One of the most well-known sites for hi-res downloads. Has a lot of re-mastered popular artists and famous albums.

iTrax
Genres
: Acoustic, blues, rock, jazz, classical, country/folk, electric/instrumental, vocal, world, crossover, R&B.
Formats: CD Quality, Hi-res, 5.1
Notes:

Linn Records
Genres: Classical, jazz
Formats: CD Quality, Hi-res.
Notes: Huge collection as well as physical media.

Magnatune
Genres: Classical, New Age, Electronica, World, Ambient, Jazz, Hip Hop, Alt Rock, Electro Rock, Hard Rock.
Formats: CD Quality
Notes: Unlimited download subscription service.

MA Recordings
Genres
: Classical and country-specific.
Formats: Hi-res.
Notes: DVDs with hi-res audio files only.

Nativedsd.com
Genres: Jazz, Classical, New Age, Acoustic, Various others
Formats: DSD64/128/265 as well as DXD

Naim Label
Genres
: Classical, jazz, contemporary.
Formats: CD Quality, Hi-res.
Notes:

Reel to Reel
Genres
: Classical, jazz, vocals.
Formats: CD Quality
Notes: $10 Annual subscription service. Members' area is not updated regularly and many files are WMV movies, but worth it for their direct-from-tape recordings.

Reference Recordings
Genres: Classical, jazz, vocals, test disks.
Formats: CD Quality, Hi-res
Notes: No downloads. Audio CDs and DVDs with hi-res files only.

Qobuz
Genres: Classical, jazz, country, pop, rock, French music, soul, funk, rap, electro, world, soundtrack, children, diction.
Formats: CD Quality, Hi-res.
Notes: Limited to Europe and the USA.

Sound Liaison
Genres: Classical, vocals and other acoustic.
Formats: DXD, DSD and lower.
Notes: Free sample in all formats from CD Quality up to 256 DSD and DXD.

2L
(See menu top-right for the listings on Klicktrack.com)
Genres: Classical (Norwegian artists)
Formats: CD Quality, Hi-res.

Classical music only:

Chandos Labels
Formats: CD Quality, Hi-res.
Notes: The Chandos site sells physical media and downloads are available from The Classical Shop (see next link).

Channel Classics Records
Genres: Covers all classical genres including vocal/opera, baroque and chamber.
Formats: DSD, CD and higher res quality FLAC, MP3, and a variety of physical media including CD and SACD
Notes: Quality formats are in 4 main types - MP3, CD (44.1/16 or 44.1/24), Studio Master (96/24) and Studio Master HD (192/24)

Dacapo Records
Formats: CD Quality, Hi-res.

Deutsche Grammophon
Genres
: Mostly classical, with a some jazz and other recordings.
Formats: CD quality FLAC, 320kbit MP3, and a variety of physical media.

eClassical
Formats
: CD Quality, Hi-res.
Notes: Download, CD and SACD.

Gimell
Tallis Scholars' Renaissance music.
Formats: CD Quality, Hi-res.
Notes: Also available from Linn Records. Their reproductions of Renaissance music are thoroughly researched and excellent.

Hyperian Records
Formats
: CD quality, Hi-res.
Notes:

The Classical Shop
Formats
: CD Quality, Hi-res.
Notes:

Presto Classical
Genres
: Covers all classical genres including vocal/opera, baroque and chamber.
Notes: MP3s, FLACs (assorted quality), and CDs.

Pristine Classical
Genres
: Mostly dedicated to out-of-print vinyl-to-digital classical remasters using XR Remastering; some jazz and blues titles following the same XR Remastering process.
Formats: High-quality MP3s, FLACs (mostly CD quality, some hi-res quality), and CDs.

The Philadelphia Orchestra
Notes: Available through HDTracks.

Free track downloads:

Archive.org
Genres
: Various
Formats: CD Quality
Notes: Has a huge live music archive that is very worth exploring.

Bravura Records
Genres
: Christmas (others later).
Formats: CD Quality (Hi-res in the future)
Notes: Direct studio recordings.

Blue Coast Records
Genres:
Formats:
CD Quality, Hi-res, DSD
Notes: Whilst primarily a commercial site,Blue Coast also has a free download section that can be accessed here

LessLoss
Genres: Classical and percussion.
Formats: 24 bit 96 kHz or 16 bit 44.1 kHz (CD Quality).

2L
Genres
: Classical (Norwegian artists)
Formats: CD Quality, Hi-res, DSD, DXD




Credit to Jazzfan, ManAtWork, opus111 and Brooko who previously added info to other articles with some of these links.