It's commonplace to see wooden dining tables surrounded with plastic modern chairs or brightly colored mismatched chairs or even intermixed fabric patterns, but you rarely see mismatched wooden chairs with a wooden table. Even adventurous decorators tend to be wood purists, and an oak table with pine chairs can look off, if not combined correctly.
The key to mixing woods is contrast. The contrast can be subtle or distinct, but it should be discernible. If you have a light wood for your table, like maple, think about using dark walnut chairs. If you have a pine vintage table with ornate carvings think about combining it with sleek modern chairs of a similar color.
There are no rules when you are breaking rules, but remember that you want your mixing to be eclectic and cool not a hodgepodge mess. To avoid a junky look, don't mix woods and then mismatch chair patterns. This can be extremely tricky. Only take on this challenge if you are a master designer.