Varies by animal and situation. I try and hunt with most of my rifles, at least a little. Here's the jist of it, I'm sure I'm forgetting a few.
Elk:
1.Winchester Mod 70 in 30-06 with an old Weaver K4. This is my main elk gun.
2.Marlin 1895G in 45-70. Has a Weaver V3 on it. Backup elk gun, and sees some coyote stands
3. Winchester Mod 70 in 270WSM with a Zeiss 4.5-14x w/ target turrets. For long range work on deer and elk.
Deer:
1. Winchester mod 70 in 243 with a Nikon Monarch 4-16x w/ hunter turrets. My go-to deer gun, also has whacked a bunch of coyotes.
2. Winchester Mod 70 in 270WSM as noted above.
Coyote/predator:
1. My Win mod 70 in 243 noted above was my old stand by and I still love to drill coyotes with it.
2. Remington 870 Express shooting a "dead coyote" choke and #4 buck. Love shotgunning predators.
3. Just got an AR, 20" bull barrel w/ Vortex 3-9x scope. It is not yet bloodied.
4. Just got a Ruger 77/22 in 22 hornet w/ an old Weaver K4. Also not bloodied.
5. Marlin 1894 in 45 colt with Skinner peep sight. Has seen quite a few stands, bagged at least one coyote. It's fun to take out.
Birds/rabbits:
1. The 870 for birds historically, although I picked up some more scatterguns recently:
2. Stevens mod 12 in 16ga, side by side. Killed a few rabbits with it.
3. Have a used 870 wingmaster on layaway w/ 3 chokes. It'll see some action for birds I reckon.
Squirrels:
1. Ruger 10/22 with 3-9x bushnell. I've killed a whole nuch of tree rats with this thing.
2. Marlin 39A 22lr with an old Weaver (B1 I think). Scope is kinda blurry but I still managed a few squirrels with it this year.
3. Unknown brand .410 I just inhereited from my late Grampa. I don't like shotgunning squirrels but it comes in handy sometimes and I like to use it.
4. Marlin 25M in 22mag with 3-9x Tasco. Usually way more gun than needed, but for long shots it occaisionally comes in handy.