This solution only works if the container is connected with a single network. The --format option of inspect comes to the rescue.
Modern Docker client syntax is:
docker inspect -f '{{range.NetworkSettings.Networks}}{{.IPAddress}}{{end}}' container_name_or_id
Old Docker client syntax is:
docker inspect --format '{{ .NetworkSettings.IPAddress }}' container_name_or_id
These commands will return the Docker container’s IP address.
If you are on Windows, use double quotes " instead of single quotes ' around the curly braces.