Oh yes, you can generate electricity from wood.
Wood has actually been used as fuel for cars. You need a wood gasifier.
Usually this is a DIY project, because cars that run on gas are very impractical, as the gasifier is heavy and takes lots of space. Similarly, you should be able to modify a gasoline powered generator to use a wood gasifier as its fuel source instead of running on gasoline.
The efficiency will be terrible, though, and it's a high maintenance work to maintain the composition of the gas suitable for continuously running the generator. I'd say this isn't something that's good for commercially selling. We won't see any wood-fired commercial generators.
On large scale, coal-fired power plants can actually be modified to run on wood. However, coal-fired power plants are dying for a good reason, they are dirty and their efficiency is poor, and the generation is very inflexible, good for mainly baseload. If you run it using wood, it's still dirty (although the carbon dioxide is from biological sources so it doesn't cause global warming but otherwise it's dirty, causing lots of pollution) and the efficiency is poor. It's also good for mainly baseload. Natural gas fired combined cycle plants have displaced coal plants for a good reason: they are flexible and efficient.
In theory, integrated gasifier combined cycle plants could have some of the benefits of natural gas plants, while still being able to run on wood. They are expensive, though, and not a large-scale solution to the electricity generation problem because we will run out of wood if they are used en masse.