Tallymonster- I'm not nearly as eloquent or concise as Travcoman45 but you can't smoke with any coniferous (firs, pines, cedars, spruces, hemlocks etc.) tree wood because they have natural resins (pitch) to protect themselves from insects and disease. These trees are naturally fragrant but make terrible smoke wood (plus creosote).
Generally, you can smoke with most hardwoods although some like walnut and elm don't seem to smoke well (and also make lousy firewood). Oak, maple, hickory and pecan, and alder all do well. Mesquite is in this group too.
Also, most North American fruit woods are outstanding because they give off a delicate sweet flavor and can be used as smoke wood by themselves or mixed with any other smoke woods especially hickory (pecan), maple and oak. Most popular seems to be apple & cherry although many smokers love pear, peach and apricot.
For woods outside the norm try vine maple, and grape vine cuttings. If you are near a vineyard many owners will give you all you want in the spring after they prune back after winter. Traeger also offers pellets in onion and garlic which aren't wood and are always mixed with other woods just for a subtle flavor. I personally haven't tried these yet.
The choice of woods is a personal one and always sets off a lively debate. Certain woods seem to pair better with certain meats but the rules aren't hard and fast. If you are thinking of smoking a particular type of meat ask for recommendations on this forum and you will be flooded with great ideas. Don't get in a rut, try different woods and mixes.