LONDON -- Every investor dreams of that elusive 10-bagger -- the stock that multiplies every pound or dollar you invest by 10. You might think this only happens with smaller companies, but given time, the FTSE 100 can serve up a few 10-baggers as well -- or, in some cases, 20-baggers.

At least 10 stocks on the index have delivered a total return of 1,000% or more over the last decade, including one 20-bagger, according to research by Fidelity Worldwide Investment. And the top three are...

Rolls-Royce Holdings (RR 2.06%)
If you had invested in aeroplane engine maker Rolls-Royce 10 years ago, in March 2003, you would be purring over your total return of 2,098%. Talk about a Rolls-Royce performance. That's what you get when a company delivers 10 successive years of profit growth and you reinvest its dividends year after year to turbocharge that growth. When they say the British can't do manufacturing, Rolls-Royce shows we can. It isn't just good in the air, with its civil and defense aerospace business; it also outperforms on land and sea, working across marine, energy, and nuclear.

Rolls-Royce doesn't just make stuff. It also has a hugely profitable range of comprehensive service packages for managing engines throughout their life cycle, giving it solid, repeat income. In 2012, its order book increased by 4%, its underlying revenue grew by 8%, and its underlying profit jumped 24%. Add to that a 60 billion pound order book, and the next 10 years look promising as well. Back in 2003, you could have bought it for 64 pence. Now you have to pay 1,022 pence. The yield isn't fantastic at 2.2%, and you aren't getting a bargain at 14.7 times earnings, and, naturally, there is no guarantee that it will rise another 1,000% over the next 10 years. But if the latest bout of eurozone turmoil causes a market sell-off, you might want to rev up your engines.

ARM Holdings (ARM) (ARMH)
In second place lies technology powerhouse ARM Holdings, which has delivered a total return of 1,848% in the last 10 years. A decade ago, you could have picked it up for 50 pence; now it would cost you 939 pence. For me, ARM is the stock that got away. I briefly owned it three years ago, only to sell in a fit of impatience. It has quadrupled in value since then as the smartphone chip pioneer rode the technology rollercoaster to fresh highs. Never go back, the saying goes -- and with ARM's mind-boggling price-to-earnings ratio of 63 times earnings, I'm certainly not going to. But with forecast earnings-per-share growth of 27% this year and next and an operating margin of 36%, you may wish to try your ARM. Citibank is still keen: It has just upped its target price from 835 pence to 1,070 pence, and it rates this stock a "buy." Credit Suisse and Goldman Sachs have respective target prices of 1,130 pence and 1,250 pence. I can't bear to go back. You might feel differently.

Aberdeen Asset Management (ADN)
The third-best-performing stock on the FTSE 100 over the past 10 years is Aberdeen Asset Management, up a stonking 1,780%. You might have thought all that market turbulence would pummel a fund manager, but not a bit of it. A decade ago, Aberdeen stock traded at 54 pence; now it costs 425 pence. Aberdeen has established itself as a renowned emerging-markets specialist fund manager, building its reputation on the BRICs. The market loves the stock, and with good reason, although this leaves it trading at a pricey 17.4 times earnings with a modest yield of 2.7%. I wouldn't buy at the price, with the recent bull run apparently slowing, but any eurozone-inspired market turbulence could serve up a great buying opportunity. If you're looking to invest safely in Beijing, Delhi, Moscow, and Brasilia, you might want to start your journey in Aberdeen.

A thousand reasons to invest
There's a reason why the FTSE 100 has thrown up these impressive multibaggers over the last 10 years. A decade ago, in the wake of the dot-com bust, the index had just bottomed out at 3,287 -- nearly half today's value. This reminds us of two very Foolish lessons. First, the best way to invest is to buy strong and solid companies when markets are down, investors are pessimistic, and stocks are going cheap. Second, ignore short-term volatility, reinvest those dividends, and be patient -- you will get there in the end. The next 10- and 20-baggers are out there.

A strong and growing dividend, carefully reinvested, can also drive long-term growth. That's why Motley Fool analysts are getting excited about one of the best income stocks on the FTSE 100. To find out what the stock is, simply download our free guide "Power Up Your Portfolio." Don't hang about; download it now while it is still free and available.