For a cash-out refinance there are several, the most glaring being that you are further indebting yourself. For a standard rate reduction refinance, the drawbacks may seem less obvious, but are still important in determining whether or not to refinance. 

Elongation of your Mortgage: 

If you have been steadily paying on your standard 30 yr mortgage for the last 10 yrs, you are only 20 yrs away from being mortgage-free.  By refinancing into another 30 yr mortgage, you may be reducing your rate and lowering your payment, but you just tacked on another 10 yrs of payments. 

On a debt consolidation refinance, while they are constantly touted as an immediate plus to your financial health, it isn't all positive. While your mortgage rate is bound to be substantially less than your credit card interest rates, a mortgage is also being paid over 30 yrs. With a credit card, if you are not continuously racking up debt, then it would be paid off in about 2 yrs at the minimum payment.  We saw plenty of maxed out credit cards in Las Vegas, and by putting them on your mortgage, the reality is you are just borrowing from Peter to pay Paul. 

Resetting the Principal/Interest Ratio:

This factor is typically overlooked, but is extremely important when deciding to refinance.  At the beginning of your mortgage you are paying almost entirely interest.  The banks set the payments up this way so that they collect as much interest as possible before you sell or refinance your home.  On a typical $1000 mortgage payment, only about 10%, or $100 a month, is applied to your principal balance. By yr 29 of your mortgage, the opposite is the case, where $900 of your payment is applied to your principal balance and only $100 goes to the interest. 

So, if you are 10 yrs into your mortgage, then about 20% of your monthly payment is being applied to principal.  By refinancing, you are resetting this ratio back to the original 9 or 10% and whittling away at your principal at half the speed you were before. 

Fees 

Unlike a purchased money mortgage, the fees on a refinance are simply tacked on to the mortgage's balance, so you don't feel the pain of having to pay out of pocket.  However, fees can typically run 2% to 3% of the mortgage's balance, and by refinancing, you are adding as much as a yr or two to the life of your mortgage. 

Bankapedia's Take

In a nutshell, do the math. If you are in dire need of a reduced payment--even with the long-term drawbacks of a refi--it beats foreclosure. If you are simply looking to save some money, a refinance isn't always roses and sunshine, like lenders will tell you.