Yes and no.
Ashes from fireplaces and wood burning stoves are a good source of potassium and a lesser source of phosphorus and some micro-nutrients, depending on the type of wood burned. So if your soil has a potassium deficiency, wood ashes can be a good amendment.
However, they can also be a source of heavy metals that you don't necessarily want in your garden. And they contain a good percentage, about 25%, calcium carbonate, an ingredient in garden lime. If your soil is very acidic (5.5 of lower), wood ash can improve your soil pH. If your soil is neutral or alkaline to begin with, adding wood ash could raise the pH high enough to interfere with plants ability to take in nutrients. Wood ash should also be avoided around acid loving plants like rhododendrons and blueberries.
Bottom line is that a small amount of wood ash will add some nutrients and be beneficial to most soils. Large amounts should be avoided.