Are you thinking big? Like, really big? That is to say, are you looking to turn a tiny amount of money now into a seven-figure stash later?

Never say never. Not only is it possible, it happens more often than you might think. The key is time and picking the right stock, of course, and then remaining patient enough to continue holding that ticker through the rough patches.

With that as the backdrop, here's a look at three familiar stocks that turned a $1,000 investment into $1 million, if not more. Just be sure to read through the wrap-up that explains what you can learn from these three enormous winners to repeat the feat in the future.

1. Amazon

Amazon (AMZN -0.07%) isn't just a familiar modern-era winner. It's arguably the market's most memorable winner of all time! Shares are up more than 230,000% just since its 1997 initial public offering (IPO) at a split-adjusted price of $0.075. A $1,000 investment in its IPO would be worth around $2.3 million today. That growth has also made Amazon one of the world's biggest companies, as measured by market cap.

It's not exactly a secret as to how it happened. Founder and longtime CEO Jeff Bezos saw an opportunity in the internet's infancy, viewing it as a convenience-providing platform where people would eventually do a great deal of their shopping. And he was right. The e-commerce giant alone accounts for over one-third of the United States' total e-commerce sales. That's bigger than the next nine e-commerce platforms combined.

It's not just an e-commerce giant anymore, though. It's also a cloud computing powerhouse. Amazon Web Services generated $90.8 billion worth of business last year, turning $24.6 billion of that revenue into operating profit. This arm now makes up roughly two-thirds of the company's entire bottom line. And again, it's a business built from scratch simply because Jeff Bezos saw a budding opportunity and acted.

2. Procter & Gamble

Tech-driven growth isn't the only path to riches, however. Consumer staples can do the job, too. Take Procter & Gamble (PG -0.19%) as an example. It, too, has made plenty of millionaires out of relatively small investors.

OK, there are a couple of important footnotes to add here. One of them is that it's taken Procter & Gamble a lot longer to turn a $1,000 investment into $1 million ... several decades longer, to be clear. Second, reaching this seven-figure mark with P&G would have required reinvesting its dividends into more shares of the stock.

Slow and steady wins the race, though.

Of course, Procter & Gamble also had an unfair competitive advantage. It's owned market-leading brands ranging from Tide detergent to Crest toothpaste to Dawn dishwashing liquid for the decades in question. Not only is it easier to maintain a lead you already own, but being a market leader also provides leverage when it comes to keeping competitors in check and distribution partners in tow.

Regardless of the reason, P&G has paid off for patient investors.

3. Apple

Last but not least, technology giant Apple (AAPL -0.62%) has also minted many patient millionaires. The stock's present price of $175 is nearly 175,000% above its split-adjusted IPO price of $0.10 per share. A $1,000 investment in its 1980 IPO would now be worth just under $1.8 million.

Granted, Apple's not been a red-hot winner for its entire existence. The company very nearly went bankrupt back in the late 1990s. It required a $150 million cash infusion from Microsoft and the rehiring of Steve Jobs as CEO to turn things around. And even then, things remained a little wobbly for years; the dot-com meltdown of 2000 certainly didn't help matters either. Apple shares didn't make any net progress during this turbulent time.

Rather, the bulk of the stock's enormous gain has taken shape since 2007, when the very first iPhone was released. It's not a stretch to suggest this incredibly popular smartphone, in fact, is the crux of the reason for the stock's incredible gains.

Whatever the cause, congratulations to the people who understood what a game-changer the iPhone would end up being. It's not just the mobile phone all other phone makers are hoping to compete with. It mainstreamed the very idea of carrying around a web-connected mini-computer in your pocket.

3 key takeaways for investors

The bad news is it's unlikely any of these three stocks can repeat the feat in the same amount of time they first turned $1,000 into $1 million (or more). All three companies are still outstanding. But circumstances were different when each stock began its heroic run-up.

The good news is, however, that the reasons Apple, Amazon, and P&G shares performed so well for so long are clear. Lots of other companies behind stocks that haven't yet dished such rallies exhibit these same qualities or soon will if they don't yet. Three of these attributes stand out above the rest.

One of these characteristics is a clear competitive advantage. For P&G, it was sheer size, which also ended up being the case for Amazon. For Apple, its edge was a superior product that other manufacturers would often imitate but would never successfully duplicate. Apple also benefited from the fact that it enjoyed complete control of the underlying digital ecosystem -- iOS, the App Store, and more -- that made its devices so functional.

Another somewhat related quality of these companies' businesses and core products is that each was and is future-proof. It's an overused example, but it still makes the point perfectly ... it was only a matter of time before someone came up with a way to circumvent the need for camera film, developing technology and at-home tools that could do the job just as well.

Conversely, the companies behind high-performance stocks aren't in jeopardy of becoming obsolete. Consumers will perpetually want newer, more powerful tech and will always want to shop. They'll also need to wash their clothes or brush their teeth. That's why you should be looking for companies that will remain relevant forever.

Finally, bear in mind that at least two of these three companies -- Amazon and Apple -- seemed a little out of the ordinary at the time their stocks were getting started on their big gains. We now know they weren't odd, however. These companies were just ahead of their time. The market's next enormous winners will likely look similarly odd. Just look a the bigger picture, considering how consumers and corporations will see their solutions 10 and 20 years into the future.