September 17, 1991

Linux is the software used for an open source operating system. That means anybody can improve it, as opposed to the operating systems familiar to most folks: Windows and Apple. Linus Torvalds is the main energy behind Linux. Linus Torvalds was born in Helsinki in 1969, though his parents are part of an Swedish enclave in Finland. Now he, and his family (wife and three children) live in Portland, Oregon. 

Torvalds explained in a Google Plus post that to specify a birthday FOR Linux, there are several options:
....Aug 25, 1991 was the date for...[the] original pre-announcement, but there's a few other relevant dates that may be even more relevant as "birthdays of Linux".

The actual 0.01 code release was September 17. But while it was uploaded to a public site, there was no public announcement of it. So in that sense Oct 5 might be the true "coming out" date - that is when 0.02 was done, announcement and all.

But you know what? You can have cake on any of those three days (or eat it continuously for the whole range). 

I assume Torvalds does not feed his cat cake. Here is a picture of his cat (at least it is a picture he himself posted in 2012.) 

Pretty cute. Linus Torvalds's cat is named Minky.