I have read a couple of his books, and listened to his show a few times. He makes alot of good points, although I don't entirely agree with everything he says. Basically, he says you should get completely out of debt and live within your means. Pay off the car, the house, the credit cards, etc. That is great advice for what his target audience is, which is people who may be having some financial difficulty.
Where I would disagree with him is that people should be worried about paying off their house quickly. There is nothing wrong with paying off your house, but if you do you are going to lose the tax advantages of being able to deduct mortgage interest, unless you are not paying enough interest for it to matter. That money used to try and pay off the house could be put to better use by saving it in my opinion.
Dave Ramsey's advice and philosophy is as sound as you can find. It is practically a guarantee that if you follow his system, you will be financially set later in life. The problem is that his advice requires a huge amount of self discipline and a postponement of buying all the hotest toys, cars, houses that the credit system will lend you the money to go in debt for. It seems that most people that have found the discipline to follow Dave's plan have first been through a financial catastrophe, and are in a position of starting from rock-bottom. Those people now know that you can "live without" for a while because that has been forced on them. If you can recognize and adopt Dave's plan before financial hardships hit you, then you will be much better off and in a much shorter period of time.
For instance, in the post I quoted above, Dave's opinion about home mortgages is the way to save you the most money, insuring that you pay the absolute minimum amount you can for your home. The 20% down prevents you from having to pay PMI insurance, which is money that you never recover. The "tax advantages" you mention (which are the tax breaks you receive against the INTEREST that you are PAYING) are minuscule compared to the amount of money you would save on a shorter mortgage. All you have to do is look at the $ amount of interest that you will pay to the bank over the course of a 30 year loan. Then, look at the $ amount of interest paid on a 15 year loan. Subtract the difference (which would be the money you avoid paying the bank) and then calculate what that money would earn you over those second 15 years if you had it invested in a mutual fund. Even a very, very conservative growth (profit) due to a slow stock market would still blow those "tax advantages" out of the water.
Much of Dave's advice has to be understood within the framework of his entire financial philosophy. Take life insurance: you will hear Dave say that the ONLY life insurance he approves is "term life." Term life means that you pay the insurance company for a policy worth $X for a term of so many years (20 years is a typical term.) How it works is that at the end of the term (20 years) if you haven't died, the insurance company owes you nothing. Your policy is over and both you and the insurance company walk away from the deal. If you are young, you can buy term life dirt cheap. On "whole life" insurance, you pay higher premiums, but the policy builds "cash value" over its life (which means that the insurance company invests your monthly payments for all those years, earning 10%-15% on them, then pays you back a tiny fraction of those profits when its over.) It's pretty clear to see why Dave would recommend you keep that money earning for you, rather than giving it to the insurance company. However, self-discipline again is a key part of Dave's plan: to use term life properly, you need to be "self-insured" by the time the term expires. That means you have a savings/retirement plan that you funnel your money into so that you have enough saved to support your family in the event of your death. If you only take half of Dave's advice and buy the cheap term insurance, but then blow the money you are saving in insurance premiums, then you will be in serious trouble at age 55 or 60 when your term insurance expires. You won't have enough saved to provide for your family, and (if you can even qualify) the premiums for a new life insurance policy will be too expensive.
My point is you can trust Ramsey's plan, but you'd better jump completely in and follow his entire model for personal finances. If you try to pick out the bits and pieces that sound good (i.e., "term life is cheaper than whole life") without understanding all the implications, then you might find yourself in trouble.