I'm not sure if "expect" is the right word, but I know I will inherit. I am an only child and my parents talk very openly about the fact that everything will be left to me (and possibly DS, their only grandchild). My dad is an only child too and inherited his parents' estate in full, and that of an unmarried great aunt. My mum also inherited the estate of an elderly neighbour who had no family when I was 5, so we moved and they then had no mortgage. None of these estates were particularly large, but cumulatively they add up to a good sum, and meant that my parents were able to send me to private school from 11.
My parents live very frugally (by choice). They never had a lot of money when I was very young, but due to these inheritances, constant saving, hefty pensions and savvy investments they are now worth quite a bit. My mum is very cautious and likes to save, so that if they need to go into a home or seek private healthcare there will be no issues. Neither are really interested in money and are comfortable living a very ordinary life. They are afraid of debt and just save. Their house could do with modernisation, they have a small car, very rarely splash out on luxuries and only go on holiday once or twice a year, but this is their choice and they are happy. A lavish, flashy lifestyle doesn't interest them.
They often remind me that when they are gone I will receive everything and have arranged power of attorney and provided details of where all of their financial/legal deeds are stored. My mum jokes that when they've gone we'll be able to afford to move to the area which I would love to love in. I hate the thought of them not being here, but I think it's important to have an idea of what the future may hold financially and to be realistic. I know there are trust funds, etc, for my son, so it's good to know that he will be financially secure.
I work full time and do have a pension, but I don't worry too much about paying in extra.
I know I am very lucky and am very grateful to them for all they have given me. In turn, I hope that we can do the same for my DS (also an only child).
DH comes from quite a large, dysfunctional family, so I doubt we would inherit much, if anything, from his side!