Is there any way at all to pay for your mortgage? Could you do it if you really tried?
Assume yes, then keep paying it.
Assume no, (loan reset, job loss etc.) go to your lender. Ask them if they can modify your loan. See if they will work with you to help you stay in it. Take your documentation with you. Income, expenses etc.
If they agreed, work with the new loan, and pay it faithfully.
if not, ask about deed in lieu of foreclosure. Give them the deed and walk away. Short sale and foreclosure are the only other options I keep seeing here. (not a lender or dealing with them)
If you can short sale keep making your payments. It may save much of your credit.
If you are going to lose it to foreclosure anyway what difference does making the payments create? Your fico score will be terrible anyway.
Keep paying on your mortgage as long as there is a chance you could keep the house. Once you stop payments you hurt your credit. It can take a very long time to rebuild it. A short sale is always said to hurt you less than a foreclosure. If you make payments on the place and do a short sale you may be able to get out from under the house before it is foreclosed on. That could mean your credit is much better than if you just foreclosed.
One last thought, if you are sure you are going to lose this house and need to rent get the rental before you face the foreclosure. Many will check your fico score when renting out and that foreclosed house could cost you a good rental.