The .32-20 cartridge came very close to becoming what the .38 Special became, the "standard" police round of the era. It was popular as a police round and small game cartridge, and since it could be mated with a Winchester rifle of the same caliber, Colt made quite a few SAAs and Official Police Models. S&W made a number of their K-Framed revolvers for guard use during WW II.
Not too much in factory, but it can produce some sizzling performance when carefully handloaded. Another favorite is to have a Ruger Blackhawk in .30 Carbine w/ auxilliary .32-20 cylinder.
It's a popular caliber for Cowboy Action shooting and brass and bullets are readily available. What I heard was once the west was basically tamed, the need for larger calibers wasn't as intense so Winchester came up with (1882) the 32WCF as a small game caliber for varmints and deer. I have a pair of clones and a Marlin in 32-20 I shoot occasionally in competition.