Eve (and others)- I read Dave's book and watched a lot of his television episodes and have a lot of trust in the guy but don't personally follow everything he says. As mentioned above, Dave is strongly against debt, referring to debt as "slavery". This includes Real Estate Debt. Dave also pushes the importance of living within your means, not on credit cards, and being financially smart.
As Jon pointed out above, ROI is not the best when you pay for a property in all cash. No one can argue with that, but it is definitely safer. One of Dave Ramsey's quotes is "100% of foreclosures last year happened to people with mortgages". Very True.
So we investors can argue all day that the ROI is better with leverage, but hundreds and thousands of "investors" are flat broke right now and bankrupt because of leverage. We are not beyond getting greedy during the good times, and losing it all when things get rough. And I know I and most every other investor will say "yeah, but I'm smarter than that" but in fact, nothing is guaranteed. Dave Ramsey's approach is not just for the paycheck to paycheck people, as others have said, but rather for everyone.
So my approach is this: Be smart, don't over-leverage (listen to people like Jon and pay homage to the 50% rule), and take Dave Ramsey's approach as much as possible: have an emergency fund, create a budget, tackle (snowball, as Dave says) your credit card debt, and stop living beyond your means.
I try to live "Dave Ramsey Smart" in my personal life but I treat my real estate investment exactly as it is - with risk. I understand that I may lose it all someday (I hope not though) but I hope to pay my personal house off and all personal debt as soon as possible so if I do go broke investing, I won't be on the street or working at McDonalds. Will I be as rich as the guy who leverages his personal house at 110% and reinvests it in his portfolio? Probably not. But I'll never lose everything and still will end up successful.
Well, I'll get off my soap box now. I highly recommend Dave's "Total Money Makeover" book if you get a chance. Let us know what you think.