Mozart’s most famous piano concerto was his No. 21, catapulted into modern international fame with its use in the 1967 Swedish film Elvira Madigan. The version used by the filmmakers there was Géza Anda’s DGG recording with the Salzburg Mozarteum, 
from his complete DGG cycle of the complete concertos.
Originally issued in 1964, the recording boomed in sales and the cover art most collectors know features a shot from the film. I have played mint copies of both the original issue and the 1967 reissue with the famous “Elvira Madigan” cover (also “Made In Germany” tulips label) here. I feel the Anda interpretation is the strongest on record, deeply felt and beautifully phrased, with just enough lilt from the Salzburgers. (A totally deserving Grand Prix du Disque winner, before the huge sales that came with the film soundtrack.) It’s worth noting that the only other performance of the work that I consider to 
be in the same league as Anda is Andras Schiff from four decades later and with the same Mozarteum band; there really is something to the idea that culture matters, and Salzburg was and still is very much Mozart’s home. The DGG catalog is 138-783, regardless of the incarnation (the US market featured different cover art on one of those oversized heavy carboard jackets, thought the LPs were still German pressings with the original “Alle hersteller” label.” The performance is available in DGG’s “Originals” CD series (though with more the famous though not-original cover art), and the complete Anda cycle is now available in a budget package.
Compared to Anda most other performances seem lackluster. Casadesus, whom I usually admire, sounds as though he is just going through the motions with Szell and Cleveland, both soloist and 
orchestra precise as always, but a bit unfeeling with inflexible tempi. NB this is not Rameau. The sound on the 2-eye copy of MS-6695 I used here is acceptable but rather clinical, nowhere near as rich as the DGG for Anda. Apparently the only version on CD is an ancient (and probably sonically awful) issue from Sony.
Similarly, Artur Rubinstein, so poetic in Chopin and almost everything else, 
seems bored with the piece in his popular 1962 RCA recording (LSC-2634). The accompaniment from the in-house RCA band under Wallenstein is undistinguished and one may safely presume not much rehearsal time went into this production. The sound is superior to the Casadesus, but still rather flat and one-dimensional — but then again I swim against the tide in my assessment of the prized LSC “shaded dogs.” (My wife commented that it sounded “neutered.”)
I included for comparison a couple of earlier mono recordings, Dinu Lipatti with Karajan (live, 1950) 
and Moura Lympany (1954) with Menges and Karajan’s Philharmonia. The Lipatti is drawn from his final performance, with HvK leading the Lucerne Festival Orchestra, so Walter Legge’s magic aside, the poor sonics can be forgiven. I sampled both a first US pressing (Angel 35931) and the UK reissue (box set RLS-749), rather improved. Can’t speak to the CD, on EMI’s Great Recordings series paired with Lipatti’s outstanding Grieg Concerto with HvK. As a performance, Lipatti falls into perhaps the same Mozart-is-all-to-quaint trap as Casadesus. There is precision (like Casadesus) and lyricism (more than Casadesus) but little feeling. The zippy third movement rather makes up for the average musicality of the first two, but this is not a memorable performance. 
Lympany is moderately more interesting, though slow tempi rather detract from matters. I’m using US/RCA 1067, from the HMV masters, with predictably shallow sound. I can’t vouch for what the folks at Dutton Labs were able to do in their CD transfer.
Lastly is the one current artist whose version of this work is truly superb, and that is Decca’s CD of András Schiff with Sandor Végh and the Mozarteum. The performance is lively and spirited, kind and tender in the slow movement without a hint of schmalzt. The paired Concerto No. 20 is also one of the finest ever put down on record. The sound is as alive as is possible as anything the digital-only world can offer.
Riehl Records 