Generally yes as long as it is wood. However your location will determine a lot of what is allowed to burn. Some areas of the UK have smoke control zones which only allow equipment approved to burn certain products.
Wood comes in many forms.
Wood is a carbon based biological material derived from living or recently living organisms. In the context of wood biomass for fuel this is often used to mean plant based material such as trees or crops.
Wood biomass can be harvested on a sustainable basis as part of a constantly replenished crop; CO2 is taken out of the atmosphere at the same time as it is released by combustion of the previous harvest. This process is often referred to as being CO2 Neutral.
This maintains a CLOSED CO2 CYCLE with no net increase in atmospheric CO2 levels. Fossil fuels such as coal, oil and natural gas are also derived from biological material, but crucially, material that absorbed CO2 from the atmosphere many millions of years ago.