Best Sounding LPs

My primary focus is on classical music, so that's what I'll focus on in answering your request. In my experience, you can rarely go wrong with the sound quality and musical aesthetic from the following record labels. It's well worthwhile to explore their catalogues.

..Argo
..Archiv
..Astree
..Audiofon
..BIS
..CRD
..Decca (any of the Speakers Corner reissues)
..EMI (avoid Angel LPs)
..Harmonia Mundi
..Hyperion
..Lyrita
..Mercury (the Speakers Corner reissues are superb)
..Nonesuch (especially Aubort/Nickrenz productions)
..Northeastern
..Opus 3
..Proprius
..Telefunken
..Titanic

Recording engineers who almost always deliver outstanding sound quality, and whose recordings I will buy without hesitation, include:

..Mark Aubort (Nonesuch and others)
..Bob Auger (CRD, ASV, Hyperion and others)
..Tony Faulkner (Decca, Hyperion and others)
..Antony Howell (Hyperion and others)
..Peter McGrath (Audifon, Harmonia Mundi)
..Jean-Francois Pontefract (Harmonia Mundi)
..Kenneth Wilkinson (Decca, Lyrita)

As to some specific recommendations of excellent performances in superb sound, I'll offer the following random recommendations for you to consider:

~ Vivaldi, Flute Concertos, McGegan/PhilBarO/J.See, Harmonia Mundi HMC 5193
~ Mozart, Horn Concertos, McGegan/PhilBarO/Greer, Harmonia Mundi HMU 7012
~ Stravinsky, Firebird, Dorati/LSO, Mercury SR 90226 (Classic Records reissue)*
~ Sibelius, Sym 2, Barbirolli/RPO, Chesky CR3
~ Berlioz, Symphonie Fantastique, Freccia/RPO, Chesky CR1 (one of the great symphonic recordings, and greatly overlooked)
~ Rachmaninov, Piano Concerto 3, Dorati/B.Janos, Mercury SR 90283 (Speakers Corner reissue)*
~ Respighi, Ancient Airs and Dances, Dorati/PhilHung, Mercury (the Golden Imports pressing sounds just fine)
~ Holst, The Planets, Previn/LSO, EMI ASD 3002
~ Charpentier, Te Deum, Christie/Les Arts Florissants, Harmonia Mundi
~ Prokofiev, Scythian Suite, Dorati/LSO, Mercury Classic Records reissue)*
~ Mendelssohn, Sym 3 (Scottish)/Hebrides Overture (Fingal's Cave), Maag/LSO, Decca SXL 2246 - 45 (Speakers Corner reissue)*

...* Currently available new; the others you'll have to find used.

Also, for an extended listing of recommended LPs based on sound quality, I agree almost point for point with Aurthur Salvatore's "Supreme Records" list. This list matched my record collection to a very high degree and I think he hits the mark consistently with his recommendations: http://www.high-endaudio.com/index_ac.html

For Jazz, look at the reissues coming from Analogue Productions, Speakers Corner and Classic Records.

Sidssp has presented a good list of recordings; I concur with his recommendations as well.

Good luck in your explorations.
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Oh, I almost forgot these.

If you could find some mint JVC CD-4 records from the 70s’, you might want to get them at once. No, they have nothing to do with CD or digital recording. CD-4 was JVC’s failed multi-channel format (4 channels to be exact), very similar to today’s Dolby Pro Logic. They played beautifully in stereo as well. In fact, I consider the engineering quality of those CD-4 records amount the best of the best. They are so quiet and durable. I bought a few 20 some years ago and I play them regularly. Some of them have been played probably close to a hundred times and still there were at most one or two pops. I don’t know how they did that. They are true engineering marvels, great stuff.

My reference for acoustic Jazz and Folk
Ry Cooder's "JAZZ" WB, German pressing.

...for Rock
Marillion "SCRIPT OF A JESTER'S TEAR"
10cc "ORIGINAL SOUNDTRACK"
Don't remember the labels of these but both pressed in Holand...

I have a number of the CD-4 records and, while some are good, most of the SQ records beat them by comparison - at least the ones I have. The grooves on the CD-4 records were very thin and some cartridges do not do well with them.

Some stated correctly that there are too many good ones (if that is possible) and there are also so many variations, even within labels, that it is somewhat hard to generalize. I would always take the "audiophile" label on an LP with a grain of salt. Some are truly audiophile, while others, a good example of which are many MFSL's, just aren't and you are much better off with the original first pressing.

Getting away from specialist and legendary pressings, try Chris Rea's "The Road to Hell"; Jennifer Warnes' "Famous Blue Raincoat"; Tracy Chapman's first album; Robbie Robertson's "Showdown at Big Sky" solo LP; Suzanne Vega's "Solitude Standing"; Steely Dan's "Gaucho"; Dire Straits "Love Over Gold", and anything by Kraftwerk or The Art of Noise for those cool-o special bass effects!