On Monday the Dow Jones Industrial Average had its single biggest one-day point drop -- a massive 777 points -- and reached a low last seen three years ago. The S&P 500 and Nasdaq are each down a minimum of 20% year to date, too -- and we're talking about broad-market indexes!

Many individual stocks have fared worse. In extreme examples, industry giants like AIG (NYSE:AIG) and Lehman Brothers(NYSE:LEH) have been brought down by excesses in financial markets, but many extremely strong franchises have been dragged down by the fear and panic surrounding the markets.

Which means …
Now is a fantastic time to be a value investor.

Really. With stocks so widely sold off, and with pessimism so pervasive, you should make like a bargain shopper and pick out a few of the values that seem to be screaming, "Buy me!"

Of course, it is always difficult to believe that stocks could possibly go up when every day they seem to edge lower. We're human, after all, and a constant downward spiral brings an overwhelming sense of loss and makes us remember prior market crashes, like the Nasdaq bubble at the beginning of this decade or the Black Monday Crash of '87.

But if those or the recent memories make you want to shun the market, sell your stocks, and move to "safer" investments, let me be blunt: That's a recipe for disaster. The market crashes I alluded to before -- dot-coms and Black Monday -- were actually fantastic times to be net buyers of stocks. So although it may seem tough in today's chaos, now's the time to go shopping, because there are many superior companies trading at discount prices.

Blue-chip bargains
I encourage investors to look long and hard at blue-chip market leaders such as Microsoft, Thermo Fisher Scientific (NYSE:TMO), and up and coming blue chip Markel Insurance(NYSE:MKL). Let's look at each of these in more depth.

Microsoft's shares are down nearly 30% from their 52-week high -- that's a bigger drop than the S&P 500 -- yet this company has one of the biggest moats I know, no debt, and absolutely no requirement to access the frozen credit markets, pays a 2.1% dividend, and is likely to buy back more of its own shares at cheap prices. No investment is perfect -- in particular I hope that ideas of over-paying for Yahoo!(NASDAQ:YHOO) have been exorcised from Bill Gates' mind -- but I can't think of many safer investments right now.

Don't be fooled by Thermo Fisher Scientific's high P/E, as this is largely the result of last year's merger of Thermo Electron and Fisher Scientific; based on this year's estimates, the P/E is a more reasonable 17. The merger has created a dominant force in the medical laboratory supply market, the company is in a relatively recession-proof industry, and it produces a ton of free cash flow. To date, the merged company has not paid a dividend, but they put their cash flow to good use, buying back $1 billion worth of shares this year.

Markel is rapidly getting the reputation of being the smaller company most like Berkshire Hathaway in its early days. Buffett is of course incomparable, but there are some significant similarities. Markel is a very disciplined specialty insurance company that will not chase premiums if rates are too low to make a decent profit. Markel's management has been in place a long time, owns a significant chunk of the company, and has a genuine concern for shareholders. Add to that their investment returns, and you can see why they get the comparison to Berkshire.

Two more options
These companies may be not quite as blue-chip as Microsoft, but they're well run and provide significant opportunities for great returns: natural gas producer XTO Energy (NYSE:XTO) and slot machine company International Game Technology(NYSE:IGT). You can get both for close to 60% of my fair-value estimate.

Natural gas prices have been almost cut in half over the last few months and -- surprise, surprise -- XTO's share price has followed suit. However, those were unnaturally high prices and not a good basis for valuation. Its management team has a history of sound capital allocation and smart acquisitions. Throw in a strong drilling record, enviably low operating costs, the potential to increase its already vast reserves, and an attractive share price, and you get a winner.

IGT has a dominant position in the rapidly growing field of worldwide gaming. Today's economic environment has made gaming more of a luxury, and consequently, the near-term growth is likely to be limited or negative. Still, the company owns roughly 70% of the slot-machine manufacturing market and has complete software systems for casino and lottery management, giving it an entrenched position that's difficult for competitors to beat. We won't always be in a recession, and IGT is well set to take off again when it ends.

But I see values today even better than the ones I just mentioned.

More values …
The historical outperformance of value investing should give you the confidence to buy in the face of pessimism. Buying superior companies at excellent prices -- and keeping an eye on the long term -- is how we advise investors at Motley Fool Inside Value.

In the most recent issue of Inside Value, I recommended two companies and ranked our top five existing recommendations for new money. As a co-advisor of the service, I invite you to take a sneak peek with a 30-day free trial. There's no obligation to buy -- and while you're there, don't forget to check out all of our past picks, research, and back issues.

This article was originally published on June 27, 2008. It has been updated.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.