You may be interested in Wood Toxicity and Allergen Chart presented at The Wood Database. With very important warning:
Just because any given wood is not listed on the chart, does not mean that it is completely safe to use. It simply means that adverse reactions have not been reported as of yet.
That said, there is over 200 kinds of wood in this one source. More in others. And that's only about wood, no say about wood smoke for smoked grain, spruce tips, et cetera. Listing all wood-related dangers is far too broad for QA format.
Only reliable way is to research particular kind you think you want to use it, and the way you want to use.
That said, some choices are known as safe.
Oak is usually OK, but don't use raw. Way too much tannins. Either use roasted oak, or chips from a barrel that had stronger alcohol maturing in it. That way tannins will either be thermally neutralized or washed out. Similar precautions about other leafy tree woods, if they have tannins in significant amount and are not on toxicity lists.
For conifers, and some leaf trees, there is an issue of resin. Some resins are poisonous. Most have bad taste. Succinic acid, acetylsalicylic acid and others may be found in amounts that can ruin the taste. Or not, depends on kind of wood, season it was cut, way it was treated when it dried, and so on.