You bet they do. Especially robins. After all that winter work posing for photos on Christmas cards and calendars, robins like nothing better than a bit of rest and relaxation in the summer sunshine.
The experts like to think that birds fan out their feathers in the sunshine in order to maintain the condition of their feathers. Tiny parasites in the feathers can cause problems with flying, insulation and appearance. The heat of the sun can dislodge these parasites and drive them to different places where the bird may have better access for removing them when preening.
But in reality it's quite likely birds just like sunning themselves for the fun of it.