My old worn out copy of the SAS Survival Manual lists the following as good tinder:

Birch bark, dried grasses, fine wood shavings, bird down, waxed paper, and cotton fluff from clothing...
Pulverized fir cones, pine needles, and the inner bark from cedar trees.
Dried fungi are excellent, if finely powdered, and scorcned or charred cotton or linen, especially ground finely, are also among the best.
Where insects such as wood wasps have been boring into trees the find dust they produce is good tinder and powdery bird and bat droppings can also be used. The inside of birds' nests are usually lined with feathers and ignite easliy-dry Fieldmouse nexts are also usable.

Whatever tinder you use MUST BE DRY. It is a good idea to carry tinder with you in a waterproof container. Always keep an eye open for tinder to collect...