I don't have any experience with the 32-20. But, was thinking about re-barreling a 44 1/2 in this cartridge. I haven't noticed anyone talking about this cartridge here and wondered if it was considered a accurate one.

I've always had a love affair with the .32-20, and I own 8 or 9 guns chambered in this caliber. I've got a Stevens 44 that is a tack driver, plus numerous Marlins, pistols, and a Ballard. 
I don't think I've ever owned a bad shooting .32-20 if the bore was good.

Having rifles in 32-20, 32H&R and 32 S&W Long, by far, the 32-20 has the most potential for top power and accuracy IMHO. The old high velocity loadings for the 32-20 will launch 115gr bullets at 1900fps where the 32 H&R will show signs of pressure at 1500fps. Now I understand that top velocities will not always make top accuracy and I rarely push max loads even though the Marlin 1894 rifles that I have will take it and more. 

If you think you need to use all the pressure room you have, go for the 32-20. A choice Charlie mentioned is the new .327 Magnum which based on early reports, may be the best choice. Pressure wise the .327 Magnum is at 40,000psi but on a 44 1/2 should not be an issue. Only problem now is that only loaded ammo is available.

Henpeckedmuch,
I beleive the differences in the answers that you are seeing is due to the fact that you have not mentioned exactly what you are looking for. Are you looking for a serious benchrest single shot capable of shooting 250's or are you thinking of a rifle to take to the woods or as a varmint rifle. Are you thinking of breech seated bullets? The difference can make all the difference in the world as far as how a recomendation goes. Hope that helps.

I've owned Colt pistols in 32-20 aka 32WCF, as I recall the 32-20 was the the 357 Magnum of it's time. The 32-20 case has a slightly tapered neck, the 32 Ideal was a longer streight-sided version of the 32-20 and used a .323 bullet. Does anyone make a reamer to cut a streighter 32-20 chamber for the .323 bullet? It seems like either the 32-20 or 32 Ideal with a .323 bullet and a turn in 14" barrel should work very well. Has anyone tried this?

Bob

Paul Shuttleworth chambered a.323 RKS barrel for my 441/2 in 32-20 that  shoots extremely well.  He also chambered a set of lyman 32-20 dies so I can resize cases and shoot case loaded bullets.  Mostly I breech seat the Hoch 207 gr. bullet,  but often for just offhand practice it is very convenient to shoot a case load.  I like it very much.  Its very happpy at velocities just under 1400 fps.  

The 32-20  CPA is pretty much a 200 yd. cartridge, and performs like the 32 Miller short.  All you do is run your 32 sizer into the mouth of a 32-20 case and you are good to go.  The powder capacity is slightly less than the Miller short.  I was shooting some case loaded off hand loads yesterday  at 100 yds., and they shot only slightly off from the breech seated loads.  A sweetheart of a cartridge for schuetzen.   
As I stated, it pretty much likes  to be around 1400 fps.  With WC820or N110 and Fed 205M or CCI BR4  primers, it will shoot under a minute of angle.  I haven't tried light squib loads for indoor shooting, but Paul says it works fine.  At 1-12, I suspect my twist is too fast for very light bullets, say 90 gr. or so.  The lightest wt mold I have is 170 gr and they work good outdoors.  Breech seated, the Hoch 208 delivers the best groups.
The thing I like about the 32-20 CPA is that is has enough neck to case load if you wish, not so for the Miller short.  Case prep is a minimum and readily available.