Do you guys use the retire button or do you have a retirement account? Or do you keep the ones that mean the most and their offspring and go from there? What about the other lines that never made it? 

All of mine are on one of two retirement accounts.

I have so many retired animals, I have one for retirees of current lines, and one for breeds I used to do, animals I've rescued from the HA, etc.

I also have so many retired animals, I keep them all on one account. I also like to keep all my animals to preserve their lines and all my hard work. xD