I prize the people I hunt with more than the things.
After that, I'd be with the guy who mentioned his dog. I mostly hunt medium game and my dog doesn't do anything in that respect, but he's still prized.
If it were to come down to equipment, then I'd have to go with binoculars.
The rifle is mostly a burden hunting and has only the purpose to end the hunt. It's only useful for the last second of the hunt. The rest of the time it just gets carried along.
I have an awesome Swaro spotter, but it's a bit of a beast on a ash Berlebach tripod with a Gitzo head. It's definitely the finest piece of equipment I have but I only use it from the 4x4. I mean, I set it up on hilltops, but I don't carry it more than a few hundred yards from the truck.
That brings up the 4x4. It's definitely the most expensive piece of equipment I have, and I depend on it immensely. I don't typically hunt from it, but I would not be able to get anywhere near where I hunt without something like it. It's a '98, so it's an older rig but I invested a lot of time and parts into it about 10 years ago and have maintained it since and it's proven to be dependable and incredibly capable.
For binos, I couldn't afford Swarovski since I need several for my family that I hunt with. I've gone with Nikon Monarch 7 so far. 8x30, 8x42, 10x42. I've also got some 7x35 Nikon porros that are heavy but hit way above their price point. More than any other equipment, this is the stuff that brings the bucks in.
I can follow the guys that mention things like boots, and jackets. That stuff is important to keeping comfortable enough to stay out. I backpack in the spring and summer, so I have good gear and enough years experience to know what works for me. Probably one of the most important pieces of clothing would be a good hat -- something really warm when needed, and something with a good brim when the sun is beating down at high altitude.
Sunglasses are pretty critical and I prize quality ones. I've used non-prescription Maui Jim with glass lenses for the last 25 years, but now I'm getting prescription. Even though it's only -0.25 in one eye (0.0 in the other), it sharpens up my vision from 20/20 to 20/15 or better. The difference is incredible, and there's nothing like visual acuity in hunting deer and antelope in the open basin and range country.
So maybe the most prize hunting possession I have is my health and eyesight.