I  couldwrite this article the usual way -- by showing you how to turn your thousands into millions through investments in solid, well-known companies. Procter & Gamble (NYSE: PG), for example, has grown by a compound average of 13% annually over the past 20 years, while Apple (Nasdaq: AAPL) has averaged 28% over the past decade! Not too shabby.

But can such returns turn your thousands into millions? Yes, eventually. A single investment of merely $10,000 would turn into $1 million in 30 years if it grew at an annual average of 17%. But that's a fairly steep rate to count on for your stock investments -- a number to which only a select few master investors can aspire. It's safer to have more conservative expectations -- perhaps closer to 10%, the stock market's historical average annual return over most of the past century.

A fine balance
So what should you do if you don't want to wait 50 or more years to make millions? Here's one option: Take a few chances.

With most of your money, you shouldn't take crazy risks. Consider socking much of it away in a broad-market index fund, such as the Vanguard 500 Index (VFINX). That low-cost fund should earn you close to the market's historical return over long periods of time. You might also try S&P 500 Depositary Receipts , an exchange-traded fund also known as SPDRs. Either of these options will instantly invest your money in 500 major American companies, such as Disney (NYSE: DIS), Harley-Davidson (NYSE: HOG), and Motorola (NYSE: MOT).

But once you've done that, take a few chances and supplement your index with growth-stock picks. That's what I'm doing in my own investment account. I don't want all of my money in an index fund, because I'd like my portfolio to grow faster than average. Instead, a chunk of my nest egg sits in a variety of individual stocks.

This strategy should help moderate volatility, and it can also allow you to do well with carefully chosen stocks. It definitely aided me in turning $3,000 into $210,000. (It can also help you zero in on great stocks the Street misses.) If you don't believe me, read fellow Fool Paul Elliott's account of how one stock can change everything. He describes how $1,800, the cost of a fancy TV, can turn into $190,000, the value of an entire home -- provided you break some rules.

Aiming for the stars
Such returns, which come from classic Rule Breaking companies, are too tempting for me to ignore. That's why I'm still on the lookout for young, dynamic companies that are breaking the rules as they grow and prosper.

The kinds of companies I'm talking about are tomorrow's Amazon.com , H&R Block (NYSE: HRB), and Wal-Mart (NYSE: WMT). Think about how different the world was before them. It would have been odd to think of storefront businesses where people would fill out your tax returns for you. We couldn't imagine buying books (and cookware and lawnmowers) on our computers. We wouldn't have been able to find low-cost discount stores in small towns across America. These are all companies that broke their industries' molds and introduced newer, better systems.

Even Ford was a Rule Breaking company once, daring to make a luxury item available to the masses at an affordable price. Just try to imagine our world without cars. Continued...