Took a 1901 Savage out for antelope does and did quite well. It was reworked into a 250-3000 at some point, but it's a tack driver. Inherited it from the father-in-law and saving it for one of my boys, but it needs some field time when the hunting isn't too rough.
Otherwise I tend to stick to newer rifles that are between 60 and 90 years old.
I have a Marlin Model 39 with a low SN, a little over 2000. Likely made in the 20's or 30's. I've not nailed the year of manufacture down, but it is the octagon bbl w/case colored receiver. I learned to shoot with that gun and hunted rabbits, squirrels and varmints with it. Love that gun. It is not mint, but still works. Here is a pic of it, and then a pic of the Marlin 39A for comparison. I have both.
I have an original 1871 Swiss Vetterli, converted to centerfire I would love to try, but, the old sights are set for about a 400 yard zero and the 10.4mm (.429) bullet has a rainbow trajectory.
My best old rifle for hunting is a 1900 Swedish Mauser, by Obendorf, Arsenal converted to Mod 38 short rifle. Also have a 1898 standard Mod 96. If I were to have to take a long range shot with original sights, my Swiss 96/11 ( mod 1896 converted to 1911 standards for their then newer cartridge).
Shotguns, a 1910 vintage Husqvarna sxs hammer gun or a 1911 Parker GH.
Another US Model 1917 user here. I got mine from my FIL. He got it from my BIL who got it from someone in California. It looks like a home sporterized affair, but it still shoots great.
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Shot a buck in Michigan last Nov with a 1904, 94 sporterized 6.5x55 Swede. I have a 96 Swede that IIRC is a 1915 model, and a 1916 Danzig mauser in 30-06. All work perfect.
I have an 1889 Remington double 12 ga. which I restored a few years ago. Going by the serial numbers the gun was built in 1893. I use a CZ .22 lr insert in the right barrel due to a bad pit in original chamber. 116 years old, but does it count as a rifle, a combination gun or a modern freak? Whatever, it's pretty cool when that rabbit-ear hammer drops and a tiny hole appears in the center of the 25 yard target.
I killed a deer with a hundred year old Winchester in .32 WS. It has excessive headspace so that was the last shot I fired through it. Worked great! It was way cool to hunt sucessfully with my great uncle's old rifle, for sure.
I have a Winchester 94 that easily beats the 100 year mark. I usually put my name and address under the butt plate and when I went to do this, I found some gent had beat me to it. So I wrote him a letter to let him know where his rifle was, not having any idea that I would ever hear back from him. About two weeks later I got a letter from him saying that he had bought the rifle used in the 1930's and hunted deer with it. He sold it a good many years and about 800 miles ago. I think he was glad it had found a home with a hunter that plans on using it. I hunt deer in close with it.