This can be one of the most frustrating issues for a wood burner. There are several causes, but it can usually be solved if you are methodical. Chimneys work on pressure differential, so you need to think about pressure issues. In general, air pressure is higher the lower you are, so the bottom of a chimney is higher pressure than the top of a chimney, so the air gets forced up. This is the same thing that makes straws work.
Chimney size - if your chimney is smaller or larger than the flue collar on your stove, it can cause downddraft. A chimney that is too small increases the flow resistance and increases the pressure in your stove. This causes smoke spillage. A chimney that is too big will cause a pressure drop in you chimney and can change the pressure dymanics again.
Competing draft - dryers, bathroom fans, range hoods, and attic fans can decrease the pressure in the house and pull air/smoke down the chimney to make-up for the exiting air. If you have an intermittent problem, check these things.
Tight houses - today's houses are very air tight to reduce energy loss. Stoves need a constant supply of make up air to "make up" for the air going into the stove/chimney. Try cracking a door or window open to see if the problem goes away. If it does, a make up air kit can be installed.
Maintenance - soot, broken tiles, air leaks in connecting pipes and other maintenance related issues can be a leading cause of down-draft.
Hills & Dales - If you live in a valley or around a lot of trees, air can get trapped in the depression and cause a locally higher pressure. This is a hard one to solve, but sometimes a power-vent can be used.
Weather & Inversions - If you have problems in fall & spring or when it is raining it could be weather patterns or a local inversion. These can usually be overcome by pre-heating the chimney or adding height. The rising heat & elevation differential should overcome the inversion.
Other - low end stoves, living in the 4th dimension, bad luck, and not going to church can sometimes cause down-draft. This can be the hardest one to solve because it usually doesn't make sense.
Call Black Duck Chimney if you are having down-draft problems, maybe we can help.
Matt Waite - Chimney Guy Owner Black Duck Chimney MI Mechanical Contractor - Specialty Wood & Gas