In my family growing up, there was a boy, 21 months, girl, 3 years (miscarriage), girl (me), 3 years, girl.
My older brother and sister were super close growing up, but I was quite close to them as well. My little sister would often play by herself when she was younger. My older sister and I fought like cats & dogs for about 5 years, then my little sister and I fought for about 5 years, and for the past 5 years my older sister and little sister don't get on (as adults). My brother is 8 years older than my little sister and they have always been SUPER close.
I think the 3 year gap is nice, because then you're never trying to potty train while another is in diapers...but at the end of the day, relationships has so much more to do with personalities and engagement rather than age, I think. Age is always an excuse to not be close to siblings, but it's just a matter of how well you get on.