Yes, you can stain wood without sanding, but it depends on the situation. If the wood is already stained and you are reapplying stain, you can stain wood without sanding.
For bare wood, it is best to sand before the application of stain. Many people make the error of sanding to grit that is either too fine or not fine enough before adding stain. If the grain is too fine, the stain will not adhere to the wood.