The short (and not entirely accurate) answer: Yes.

The real answer:

If you do not change your mortgage, the payments will be collected as they are due according to your note.

If your note is fixed, generally your payment will not change.

There are a few exceptions with fixed rate loans:

1. If your taxes or insurance are included in your payment, and one of these items changes, your total monthly payment will change as well.
   
2. If your loan has an "interest only" period (where no principal is due), and then this period ends, your loan payment will increase to include the principal that must eventually be paid back.

If your loan has an adjustable rate portion, your payment will change according to the "adjustable rate rider" in your note. Generally this means that at a pre-set interval, the rate on your loan will be recalculated by taking an index that is publically available and adding a certain amount (called your "margin").

If your loan has a "negative amortization" option - where you initially paid even less than the interest that was due as a "starter payment", your loan payment will be recalculated repeatedly throughout the loan so that you will be able to eventually pay the entire loan off. If this is the case, have someone who fully understands lending take a look at your loan documents and explain what could happen, as each of these loans is written according to specific terms.

Finally . . . if you are unable to make your loan payments and you qualify for one of several government subsidized loan modification plans, your servicer (lender) may decide that it is in everybody's best interest to reduce your payment or change the terms of repayment so that you do not lose the home and they do not have to foreclose and sell it at a loss. Anyone struggling to make their payments should contact their servicer to see if their loan is eligible for modification. The process is similar to applying for a loan - expect to provide lots of documentation. Generally it is only available AFTER you have tried to refinance and have discovered that you are not eligible for some reason.

Other than the above, generally speaking, you would need to refinance the loan to a lower rate or longer term in order to reduce your payment.

To increase the amount of principal that is being paid (or add principal to an interest only payment), simply add money to the payment each month, specifying that you desire the excess to reduce your principal - no refinance necessary.

Refinancing is the quickest and most typical route to lowering your interest rate.  However, some homeowners have been able to workout agreements with their current lender either to lock in to a fixed rate or locking in for a lower rate.  This process can be daunting and take a long time.  You may even have to prove that you are in a hardship to qualify for this sort of special agreement.  

Depending on who holds your current mortgage, FHA, Fannie Mae or Freddie Mac you may qualify for a streamline refinance.  A streamline is a type of refinance that requires little to no documentation.  Even if you qualify for a streamline you are still refinancing your home- the biggest difference with a streamline and a regular refinance is that an FHA Streamline does NOT require an appraisal or income documentation for approval.  Fannie and Freddie Streamlines DO require the same documentation on a regular refinance, however they have the ability to go over 100% Loan to Value and in some instances does not require PMI.

Right now is a great time to refinance and take advantage of the low low rates!  I would suggest that you contact your local mortgage company to see if you qualify today!  Ask the Loan Officer if you qualify for any of the above mentioned programs to get the best deal.