At a bare minimum, you should always have 10' x 2" polyester sling. You can use it to fasten the winch cable or snatch block (see blow) to a tree without damaging the bark. And the polyester will not stretch.
If space allows, you should also carry about a length of 1/2-inch double-braided polyester rope (300 feet if possible). Double-braid construction is very durable, and its low-stretch properties are safer. It’s also relatively inexpensive and abrasion resistant. And this diameter has a breakpoint of approximately 7,200 lbs. - more than enough for most jobs.
Block and Tackle
Start with a double swing side snatch block, which effectively doubles your pulling power. It’s great for simple tasks like elevating game for skinning and quartering, or for various pulling situations. The swing-side snatch eliminates the need to thread the full length of the rope through. Better models feature a deep (4-inch) groove aluminum sheave, stainless steel plates, and a stainless steel shaft. Adding a self-blocking pulley gives you a 4:1 mechanical advantage for those really tough jobs.
You’d be amazed how many uses you can find for a simple steel hook. Carry a couple with you, preferably the type with a spring-laded safety clasp to prevent slipping.
Locking carabineers have numerous uses including anchoring ropes, slings or snatch blocks. Don’t scrimp. Buy the nickel plated steel variety with an anodized aluminum screw gate lock.
If you decide to go with a portable winch rather than one fixed to your machine, you may want a few other accessories. For instance, you’ll probably want a padded, waterproof case for the winch and all accessories. A hitch plate anchor allows you to affix the winch to any towing balls up to 2'' diameter.)