My grandmother had 12 kids and 30 grandchildren - my mom is the youngest child, and I am the youngest grandchild. She died when I was six. I do think she had a pretty good relationship with all of the grandchildren, and would visit everyone, send (smallish) gifts and cards for our birthdays, and keep up with all of our lives (in fact, I received a birthday card for my birthday after she had died - she had mailed it right before she died).
However, our extended family does not have the same tightness that I see a lot of other families have - after she passed, there were no more large family holidays or anything like that.
Funerals of her siblings are the only time the extended family gets together. I think that I missed out on the experience my older cousins had growing up. Everyone sort of focused on their own families - my mom's oldest sister was 24 years older then her, so a lot of her siblings had their own grandchildren by the time I was born.
My dad is an only child, we saw those grandparents regularly until they passed when we were young adults, but they weren't warm people so I wouldn't say we had a super close relationship.