What every Indian schoolchild knows.
Humayun 1530-39, 1555-56
Shah Jahan 1628-58
Bahadur Shah I 1707-12
My mnemonic: Boys have a jolly sojourn at Bombay.
These are the main or great Mughals. The last emperor (1837-57) was Bahadur Shah II.
Shah Jahan was the builder of the Red Fort as well as of the Taj Mahal.