A step back towards the original topic...
Remember, one of the biggest differences between wealthy people and everyone else is that wealthy people know how to use money properly, and everyone else does not (or chooses not to).
There is a book, "Rich Dad, Poor Dad" that explains a lot of this stuff, including why kids of well off parents tend to remain well off. It's not necessarily because of their parent's actual wealth, rather it's because they are brought up with a specific attitude about money that leads to a lifestyle of "using" money for generic personal gain, rather than simply viewing money as something used only to buy stuff.
I got lucky... My parents raised me to view most non-essential debt as a bad thing, and also to view money as a resource as opposed to something I simply hand over to salespeople. I did just fine without my parent's forking over cash to me, and I've been very careful about debt for my whole life. Yes I used to make big purchases on a credit card, but they'd get paid off almost immediately. Very large items such as my first new car and my first house were bought with traditional loans, but I paid them off far earlier than the loan terms dictated at the same time I maxed out my yearly IRA contribution. The tradeoff was that for maybe 8 years after I started receiving a regular paycheck, I didn't have a nice TV or in fact anything else that was super nice except for a computer (duh) and a car I bought after nearly 6 years in the AF. But I have never ever had to make a tough decision because I didn't have enough money. If it was a necessity, it was budgeted for and prioritized over luxuries. If I didn't really need something and didn't quite have enough money to buy it, I usually put the money for that item into some sort of investment or interest earning savings account. By the time I could afford the item, I usually didn't want it anymore so I ended up with a nice emergency fund that went as the down payment on my first house.
The point is that although being out of debt is a great first step, the next step towards financial comfort (not necessarily wealth, but comfort) is to learn how to USE money. And the best way to start IMHO is to start up one of those automatic contribution retirement accounts. Many places will let you start with as little as $200 up front and $50-$100 per month automatic contribution, which is little more than beer/pizza money for most people. Give up something you don't need, and start putting some money away in a roth IRA or other investment/savings account. You'll learn a lot while managing the account even if it isn't very big at first, and if you're not greedy you'll have more money down the road that you didn't have to work as hard to earn.