This is the tying equipment (apart from my own tools) that I use when I tie flies. 
Law Vise–the most user-friendly vise in the world!
Rite Bobbin–bobbins with ceramic thread tubes prevent the thread from snapping.
Mine are specially made to fit very small (Persall’s) bobbins.
I fill them with tying thread using a sewing machine. 
A real must is classic surgeon scalpels with replaceable blades–one standard
size for my wing materials and a larger one with thicker blade to cut foam.
A metal ruler and a small cutting mat. 
Fine scissors is another must. In my collection you’ll find two pairs of self-sharpening
and spring-loaded mini-scissors from Benecchi–one pair with straight blades and the other
with curved blades. I also have a pair of small regular scissors to cut foam and plastic materials. 
I use four types of tweezers. A curved, narrow and sharp tweezer; plus a straight,
narrow and sharp tweezer for fine details and a bold, straight and sharp one for tough jobs,
like pulling off foam or feathers. The fourth tweezer is small and self-locking one to hold hackle and other materials. 
A small dubbing hook and a small paper clip when making loops of dubbing and hackle.
A standard dubbing needle.
An old dental tool is always useful.
A standard whip finisher to tie smooth knots when finishing the flies.
A small can with a mounted needle in the top to apply varnish.
A battery-charged hot point pen to heat, burn and shape legs and tentacles.
Waterproof marker pens Copic and Pantone: Yellow, orange, beige, olive, brown, grey (no 4, 6, 8). Also some colorless blenders to mix colors and create fadeouts.
Black pens, Staedtler pigment liner 0.05 / 0.1 and Penol 777 fine line. I use them for making eyes, segments and patterns.
Finally, a healthy dose of patience.