Are we talking savings as in you can touch it or savings as in retirement savings? Big difference there.
No easy answer to this question because of the various situations. The school one being a huge one if you go to college. Many people are faced either with loans or paying for school as they go and neither are cheap options. In my situation, I grew up and went to school in Indiana. Didn't move to NY until I was 25. I can assure you that event part time wages are much lower there. True, things are more expensive in NY, but if you live with your parents and don't have to pay for anything, you're going to save more money. I was able to pay for a lot of school as I went, but am still paying off a loan. I should have it paid off in full by the end of next year.
I think the biggest mistake that most (young) people make is not maxing out 401K opportunities through their employer. It's hard, especially if you have loans and you have an entry level salary, but there are ways to make it work. Saving for retirement in general for young people is hard. Even as a teenager, kids would be smart to put away a percentage of what they make into an IRA. Try to max it out if you can, but that's hard when you're younger.
But people should realize that everyone makes financial mistakes and what is done is done. Learn from it and don't repeat it. My biggest mistake was moving into a 1BR apartment by myself before I could properly afford it. It ended up working out ultimately, but there were some tough months.
With all that said, I think if you have $20K by the time you're 30, especially if your schooling wasn't paid for, you're doing a-ok.