I don't currently own any .44 Special-only guns (just a .44 Magnum) but this is the last one I did own:
S&W Model 21-4
I have something of a love-hate relationship with the .44 Special. I love the cartridge, I really do, but I'm not so fond of the packages that it comes in. My first .44 was a Taurus 445 snubby. While the gun worked well enough, it was DAO (which I wasn't particularly wild about) and had absolutely horrendous muzzle flip with anything but the lightest of handloads. It was sold to help finance my S&W M66.
The M21 was a much more pleasant gun to shoot, but I never could get past the gun being as large and heavy as it was without being able to shoot .44 Magnums. That gun was sold and part of the money put towards my S&W 629.
Based on past experience, I think that a S&W 696 might be the .44 Special I'd most like, but they are neither common nor cheap. If I happened to find a good deal on a Charter Arms Bulldog or Rossi 720, I might pick it up to use as a glovebox gun.