Well, it can take any larger critter on the Continental US. Might be a bit stout for squirrel, bunnies and turkey though.
It'd make a fine Homestead Defense round in the country - sure do a number on any goblins in the yard!
the question is out there, what IS 444 Marlin good for? A big bore round usually chambered in lever action rifles, firing the same diameter bullets as the 44 Rem Mag, but much faster.
It's a little demeaning to say that it's "nothing more" than a lengthened .44 mag, because that extra inch of powder buys you at least 600 fps more velocity in a comparable length barrel. That's nothing to sneeze at. In terms of muzzle energy, that extra inch causes .44 caliber projectiles to be pumped out at .30-06 power levels.
The .444 Marlin has been mildly popular up here since it came out 25 years ago. It handles any deer or bear with ease. Some folks up in Quebec use it for moose. The caliber makes a good choice for hunters not satisfied with the .30/30 or .35 Rem.
I agree that the ammo is expensive. Best to reload your own with this caliber. It's an easy case to reload (similar to the .45/70) and several bullet weights/styles are available.
the 444 is good for deer and black bear. bullet selection is the killer for this cartridge, the .429 bullets are all designed for the 44 magnum/special handguns and are not built for use in a rifle with much higher velocity.