Say I as a pianist want to play/practice Saint-Saens's second piano concerto, but I happen to not have a symphony orchestra in my living room. How can I play this? Are there "pianoless" recordings to play along with?
These types of recordings are usually called or "play-alongs" or "play-a-longs." A company called Music Minus One has been making classical music play-alongs since the 1950s. The company is now owned by Hal Leonard. They produce accompaniments for some of the most famous concertos for all instruments, including Saint-Saen's 2nd Piano Concerto. For the play-alongs, they record real orchestras accompanying professional soloists. This means you are forced to mostly use that soloist's interpretive choices, but they won't be as robotic as MIDI accompaniment, which is another option.
Play-alongs also exist for the jazz, blues, rock, and pop genres.
I can't speak for recordings, but most concertos (at least the famous ones) have a piano arrangement of the orchestra. This way, the soloist can practice playing with the accompaniment, but the accompaniment is simply someone at another piano.
As one famous example of this, consider the following comedy bit by Victor Borge that uses Tchavikovsky's First Piano Concerto.