Panama (then part of Colombia): Technically the first transcontinental railroad was the Panama Railway, completed in 1855, near the narrowest point on the continent. It is only 48 miles long.
Asia: The first Asian transcontinental railroad was the Trans-Siberian railway (with connecting lines in Europe), completed in 1905. It is the world's longest rail line at 9,289km (5,787 miles) long.
Africa: There is no African transcontinental railroad. At least two trans-African projects have been planned: the Cape-Cairo railway by Cecil Rhodes on behalf of the British Empire, and a line from Abidjan to Algiers by the French.