The way it's all connected doesn't even have to be too obvious. Three examples pop out of my mind: Stephen King, Kurt Vonnegut and Gabriel García Márquez.
All three of them have more or less a common setting, or at least an "axle" of sort that can be traced down (New England, particularly Maine; Upper NY, especially the made-up city of Ilium and Macondo, in a dream-like Colombia) and several landmarks that help settle their stories in the same universe (i.e. Mentions of The Shawshank State Penitentiary, Kilgore Trout's novels, the exploits of colonel Aureliano Buendía, etc.) but besides that, all stories are strong enough to stand on itself.
Basically, you try to keep the familiarity of the world for old readers while avoid alienating the new readers.