Thanks to the marvellous BBC programme catalogue prototype, you can – assuming you’re, er, not too old – see what was on TV on the day you were born, and even, if you know your time of birth, at the very moment you entered the world.
The link you need is in the format http://open.bbc.co.uk/catalogue/infax/on_this_day/yyyy/mm/dd where yyyy is the full year, mm is the month in two digits (e.g., 04 for April), and dd for the day.
From this we can see that the newly-thirtysomething Stephen Tall has the privilege of being born on the day the fourth episode of the fantastic Doctor Who story The Talons of Weng-Chiang first aired, while today’s birthday boy Duncan had the pleasure of a budget reply party political broadcast from the SDP/Liberal Alliance featuring Roy Jenkins.
Only one of these TV programmes featured a giant rat. I leave you to guess which