With the responses thus far, and with the possible exception of one response, I find it puzzling that the Richard Strauss recording output conducted by Fritz Reiner and Karl Böhm has been largely overlooked, or people here simply don't know much about these conductors. Both of those conductors were very close artistically and professionally with Strauss, almost identical a friendship status as that shared with Mahler by Walter and Klemperer, and both sets of artistic friendships occurred at about the same time, though Strauss lived much longer than Mahler. I could go into considerable detail about both of these conductors' Strauss recordings, as it would be beyond the scope and very much off topic to do so, but I'll make some basic comments below.
Both Reiner's and Böhm's Richard Strauss recordings are very well known, though Böhm lived longer than Reiner and had the advantage of being able to record nearly all of the Strauss operas in Europe where costs for doing that were considerably cheaper there than here in the U.S. You can hear Reiner's complete Metropolitan Opera Strauss performances of Salome, Elektra (two of each), and Der Rosenkavalier, on non-commercial, private recordings, but he wasn't able to have microphones present at his other Strauss opera performances, most of which occurred much earlier in Europe. Otherwise, you can hear Reiner's Strauss opera performances via excerpts on commercial recordings by RCA and Columbia Masterworks. Reiner also gained fame as conducting the premiere of Die Frau ohne Schatten (The Woman without a Shadow) when music director in Dresden after WWI.
If nothing else, Reiner's fame on records as a Richard Strauss conductor is secured through the very early stereo recordings he made for RCA in 1954(!) of Also sprach Zarathustra and Ein Heldenleben. These two recordings have stood the test of time and have become references as to how these works should be performed. Though Reiner was considered somewhat reserved in many of his Strauss and other composers' performances, he could generate fire, and control that fire with exactitude all at the same time without abandon. I was at a subscribers' social years ago when Leonard Slatkin was about to enter his first season as music director of the National Symphony Orchestra of Washington, DC, and I asked him what his plans were for doing recordings with the NSO. He responded that he didn't plan to record any "warhorses", and he backed up that statement by asking "Why should I bother to make a recording of Ein Heldenleben when Reiner said all that there is to say about it?"
I'll close my statements about Reiner by saying that almost all of his stereo Chicago Symphony Orchestra Richard Strauss recordings have been reissued as SACDs, for the sound on them is not only that good, and the performances are nonpareil. Also, he made some Strauss recordings while he was musical director of the Pittsburgh Symphony Orchestra in the 1940's, though issuance of these on CD were pretty much on an obscure French label, so they're hard to find, and LP issuances of them are likewise hard to find and often in poor shape and a bit on the expensive side from second-hand purveyors of classical recordings.
Karl Böhm, another renown conductor of Richard Strauss, generally tended to be more a reserved conductor than Reiner, and usually didn't deliver his Strauss with fire that Reiner did. As I mention above, most of Böhm's fame with Strauss was with the operas, though he did make recordings of Strauss orchestral works that are worth having. Virtually all of Böhm's Strauss output was recorded by Deutsche Grammophon. His recording of Also sprach Zarathustra in 1958 in stereo, was a Grammy winner.
Wade
P.S. - I forgot two other conductors who were artistic friends/confidantes of Richard Strauss, and for which recordings exist:
George Szell - He recorded some of the orchestral works with the Cleveland Orchestra and some of the songs for orchestra, including Four Last Songs, in Europe (mentioned above). Most of these were recorded in stereo for Columbia Masterworks and the vocal works were recorded in stereo for EMI in Europe.
Clemens Krauss - His output dates to the pre-stereo days in Europe, most of which were recorded by London/Decca. There are recordings of the more renown Strauss operas and many of the orchestral works, including an obscure recording of Strauss' early orchestral work, Aus Italien (From Italy). His Der Rosenkavalier is considered legendary. I don't recall exactly if any of these were ever issued on CD, but they generally go for a good price from second-hand sources.