The real question is, why do we recommend index funds to so many people here, and then, why do we recommend Vanguard's in particular?
In order to have a good shot at a secure, reasonably well funded retirement, most of us will need to have some portfolio of stocks (and bonds, but let's just talk about stocks for now; the same arguments I'm going to present for stocks apply to bonds). So how do we get those stocks?
You could pick them. That's what people did back in the day and that's what some people do now. There are various stock picking theories, and I won't go into what they are. If you're into that, great; I'm not going to discourage you from doing what you believe is the best way to achieve your financial goals. And if you beat the market, even better. But very few people will do so, and those that do will spend a great deal of time doing it (as will many that don't).
If you aren't picking stocks, you still need to have some. It's just that your best bet at that point is some sort of mutual fund (or equivalent, like an ETF, which some people seem to view as a different investment entirely, when in reality it isn't significantly different from a mutual fund. In fact, at Vanguard, the ETFs are a share class of the mutual fund). You could try to pick mutual funds that are going to beat the market within your desired asset allocation -- but given how few repeatedly do so, we're back to the same problem as picking stocks in the first place. You could find a financial advisor who will do this for you, but that selection process has the same problem. To top it off, there's all sorts of fees that are certain to eat into your total return. The odds are against you if your goal is to pick a mutual fund that will beat an index fund in terms of the return that you see (and ultimately, that's the number that matters).
Which brings us to the idea that most people here aren't going to beat the market. For the vast majority of what I'll call casual investors - people who want to set their allocation, contribute methodically, and not think about it more than a few hours a year - index funds (and the asset allocation wrappers - life style and target date funds - that use them, too) really are the key.
And since there isn't much to index funds to compare across companies, costs become the key. (I'll point out here that if you want to do stock trading, Vanguard probably isn't the right brokerage for you, although they do have some actively managed mutual funds beyond allocation ones. And once you have over a half of a million dollars in assets there, you can make very discounted trades of stocks should you be so inclined - I think it drops to like $2/trade, and at $1 million in assets, you get some number of free stock trades per year too)
So, fees. Vanguard's fees are among the lowest in the business. None of their funds charge a sales load. The expense ratios for their lowest investment minimum share class - "investor" shares - are among the lowest in the industry. And when your investment in a given index fund gets to $10,000 - a pittance in the grand scheme of things - the expense ratio drops even further as you qualify for Admiral shares (which your investor shares will get promoted to when you hit this mark).
If you're looking to diversify the portion of your stock portfolio that you want to be in domestic (U.S. company) stock, you can hardly go wrong with a total U.S. market fund. And at Admiral class, the expense ratio is 0.05%. Compared to $6.95/trade at many brokerages, you'd need less than one trade per $13,900 invested to have the same costs -- good luck not having your costs drag on your "versus index" performance there.
Note that I said "among the lowest" - there are occasionally funds with a lower expense ratio for the same product that come along. I've yet to see one that didn't feel like a loss leader, certainly not at the five-figures (or more) invested mark. On top of this, those with lower expense ratios tend to be offered by for-profit brokerages, further giving me the "loss leader" feeling as these companies lose business to Vanguard. It's only a matter of time, I feel, before the expense ratios of these creep up, or the companies offering them make up for the loss in other ways. By contrast, Vanguard runs their funds at-cost, so I know that the expense ratios I'm paying are the cost of operating the fund and that any future cost savings will go to me: they don't have shareholders (other than those who are invested in Vanguard mutual funds) who might want to claim the difference as profit.
In summary: if you aren't going to stock pick, or pick someone to pick for you, or pick someone to pick someone to pick for you, you're a good candidate for Vanguard's index mutual funds. And that's a sizable fraction of people who come here looking for advice.
I have been a Vanguard customer for over 5 years for a traditional IRA and now Roth IRA, and am extremely satisfied. I have done multiple rollovers of 401ks from different jobs, each time I just pick up the phone to call Vanguard and they walk me through it while handling as much of the work as they can.
Also, each time my balance in a respective fund has hit 10k they send me a letter to let me know I will be paying an even smaller part of the paltry fee they charge me.
I'm extremely risk averse with my retirement money and as a 33 year old I worry about my funds sitting out there for so long. Vanguard is a company that, as much is as possible in this environment, gives me confidence that they'll be around in 30 or so years when I start living off this money. To me they just come off as very classy and conservative, not to say that other companies aren't as well, this is just my experience.
I use Vanguard for buying individual stocks and pay $7 per transaction, but I'm a buy and hold investor so to me that's nothing. I'm willing to pay that for the reputation and stability the brokerage has, and it's still less than Scottrade. People shoe horn Vanguard as a index and etf brokerage but that's not the whole picture.
If you're a buy and hold investor and certainly one with a fair amount of capital, I can find no better place, just realize they're not think-or-swim so nothing fancy or high tech. I'd never use them to day trade or anything similar but for buy and holders, it works great.