Yes, so long as its woodash and not coal or coke ash. Good for flowering/fruiting plants.

Best to use in the growing season as the winter rains will quickly wash the potassium away without being absorbed by the plants. Try not to use on lime-haters, as the ash will contain calcium which will lock up magnesium and iron and cause the leaves to yellow
(Chlorosis).

Good for adding potash to the garden. Sprinkle it very thinly as a thick layer will turn into a sludge when it gets wet. It can be added to the compost heap and I use it in my potting composts to feed bulbs and the roots of plants. We have a multifuel stove which we light as required in autumn and spring (it is burning now!) burning wood only, then, when the weather really sets in we add anthracite to keep it in overnight. We only use the ash collected in the 'wood only' seasons.

Don't put it on your raspberries though as it changes the pH a bit and they don't like it. Make sure there is no anthracite ash in it. And if you store it before use, keep it dry, as the potassium is very soluble and will leach out as soon as it rains.

There's a forum on the 'Wild About Britain' site and it has a section that goes into the subject of woodburners very very thoroughly.
It's definately worth a read.

THANKS TO EVERYONE WHO REPLIED TO MY QUESTION ABOUT THE USE OF ASH FROM MY WOOD BURNER

Not sure about the "Don't put it on your raspberries" bit, Steragram. We have mountains of woodash each year, and we regularly spread it around the whole garden, raspberry beds included and we get an embarrassingly abundant crop every year. I'm sure it depends on the soil type you start off with.

Probably does. I didn't know about this advice until quite recently. Maybe I'll go back to trying it next year and see - I certainly didn't get an enormous crop this year. But my soil is only a tiny bit on the acid side of neutral.