I knew all of my grandparents and some of my great granparents. I have wonderful memories from when I was small, but three of my grandparents are still alive so am still making memories!
I guess their influence on your life is the same as anyone else's. I was very lucky, but my husband knew his grandparents and they were pretty twisted alcoholics, and not very nice people. They died by the times he was in his early teens.
Now I have a daughter of my own I am pleased that she has grandparents that adore her and want to have special times with her, but sadly, one of her grandparents is a very selfish person and does not want to be a part of our life because she can't be bothered. She won't visit us and we can't afford to keep making trips to he all the time, she doesn't even pick the phone up to ring or to even send an email, so now I think that it is her loss. I don't want my baby growing up wondering what she had done wrong that her nanny isn't interested in her, so I am focussing on the positives in her life and we will wait until her nan is ready.