Yes. My grandparents' house was left to my mum, but when they died she passed it on to my sister and I because she could see that it would benefit us. We grew up with very little spare cash - not absolute poverty, but no luxuries or anything. I think my parents were glad to be able to give us a helping hand onto the property ladder (it was at the stage when prices were really starting to shoot up).
They don't generally give us money now, although at one stage when I was having a rough time, made redundant, very depressed, they paid to redecorate my bedroom, which was really nice of them, and they took my sister on holiday as well. They have also given us their old cars a couple of times - not massively expensive ones, but for example when DS was born I was driving an 18 year old car, and my dad gave me his (10 year old one) and got himself a new one.
When my sister had a run of things breaking (boiler, washing machine and some kind of fuse box thing) they gave us £1000 each just to help out with bills.
None of us has loads of money, but they feel like they have enough to see them through and they wouldn't want to see their children and grandchildren struggling or going without heat when they have a decent amount of savings.
We've always been expected to be independent and sensible with money, which we have been, so I think they also see that we're not just going mad with it and will genuinely use it well.