Largely depends on the sort of shirt and whether one is wearing jeans or something more formal.
Polo Shirt = Out at all times
Tee Shirt = ditto
Dress Shirt = In at all times
Business Shirt = ditto
Any shirt with a "tail" = In at all times
Casual straight bottomed or "sports" shirt = Out unless you want to look like a Northerner in which case wear it in with braces to hold up your trousers.
Rugby Shirt = Out with jeans and shorts unless the referee tell you to tuck it in.
Sweat Shirt = Out at all times but should only be worn with jeans or shorts