It's a great cartridge - even better if you handload.
As far as factory ammo goes....
Companies like Buffalo Bore offer some specialty loads for the cartridge, but some of them don't have the best track records. I would avoid the specialty stuff.
The original and "classic" load for .444 Marlin is the Remington Express 240 gr Soft Point. It's a half-decent load, but I, personally, am not a fan of the bullet. It's fairly fragile for a rifle bullet, and is undersized (.444 barrels typically have .428" bores and .432" grooves -- and the Remington 240 gr SP is .429" in diameter
).
Hornady offers several different loads, in their different ammunition lines. The loads of note are:
(Note: All Hornady loads use .430" diameter bullets, that fit .444 barrels better.)
265 gr FP SuperFormance - This is THE best factory load for any .444 Marlin, in my opinion. It has the best bullet, the highest velocity, the best feeding reliability, and is extremely consistent. It'll take anything in North America, with room to spare.
265 gr FTX LeveRevolution - This works well for
some people, but not all, and is generally only recommended for deer or hogs. It is not a tough bullet, and I don't think it should be used on larger game. In addition, this load uses shorter than standard brass cases, so you'll get a carbon ring in your chamber. Cleaning that carbon out is a pain, but failing to do so can cause chambering issues with other loads. The gummy tip on the bullet can cause feeding issues in pre-2003 Marlins, and especially pre-1975 Marlins.
265 gr FP Light Magnum - Some rifles love this load. Some rifles hate it. It's a reduced load, with slightly reduced velocity, to cater to recoil-sensitive shooters, but still be adequate for big game. It uses the same 265 gr FP InterLock as the SuperFormance load, but the lower velocity seems to make some rifles throw fits.
225 gr FTX LeveRevolution - This load was a tremendous flop. It didn't work well for anyone, and the bullet was incredibly fragile. It is no longer in production, but boxes can be found on store shelves occasionally. Like the 265 gr FTX load, it uses shorter cases and causes the same problems.
That being said..... Hornady is currently only producing the 265 gr FTX LeveRevolution load. All other are temporarily discontinued, or not due for production until August (or even 2015).
One thing to keep in mind about all ammo for .444 Marlin rifles is the twist rate of your barrel.
Older Marlins* had 1:38" twist rates with Micro-Groove rifling. Most of those barrels do not do well with bullets 300 grains or heavier, and some really hate the 265 gr FTX bullet. Those barrels say "Micro-Groove" on them.
Newer Marlins* have a 1:20" twist rate with Ballard ("standard", deep) rifling. They shoot pretty much everything well, and some things (like the 265 gr FP) fantastically. Many of we 1:20" owners shoot bullets up to 500 grains, from 1,200 to 2,200 fps, without issue. Marlin 1:20" barrels are marked with asterisks on each side of the model designation. -Example: **** Model 444P - Cal. 444 Marlin **** .
*(The change happened in about July/August 1998. Before then, everything was Micro-Groove. After that, everything was Ballard.)