Currently I have a mortgage that I am underwater on by about $10K - $15k, and I am looking to move to a different state in the next year for several unrelated reasons (not buying a new home). I have about $800 to $1000 extra each month to put toward savings or principal, but I am not sure which is better in my current situation. I don't have other debt that needs to be paid off. So should I pay the extra money against the mortgage principal even though I might be in short sale situation and I would lose the extra principal I paid? Or should I keep the money in a savings account so that I have more cash for the closing?
I'd pile up as much cash as you can in a savings account - you will need money for the move (even if it's just gas money) and it's going to be hard to predict where house prices are going so you might or might not be underwater when it comes time to sell the house. Or you might be so deep underwater by then that the extra money doesn't make much of a difference anymore anyway.
Once you're actually in the process of selling the house, you can figure out if you can (or need to) use the savings to cover the shortfall, closing costs or if you just built up a little wealth during the time you put the money aside.
You say you are underwater by $10k-15k. Does that include the 6% comission that selling will cost you? If you are underwater and have to sell anyway, why would you want to give the bank any extra money? A loss will be taken on the sale. Personally i would want the bank to take as much of that loss as possible, rather than myself. Depending on the locale the mortgage may or may not be non-recourse, ie the loan contract implies that the bank can take the house from you if you default, but if 'non-recourse' the bank has no legal way to demand more money from you.
Getting the bank to cooperate on a short sale might be massively painful. If you have $ in your savings, you might have more leverage to nego with the bank on how much money you have to give them in the event the loan is not 'non-recourse'. Note that even if not 'non-recourse', it's not clear it would be worth the banks time and money to pursue any shortfall after a sale or if you just walk away and mail the keys to the bank.
If you're not worried about your credit, the most financially beneficial action for you might be to simply stop paying the mortgage at all and bank the whole payments. It will take the bank some time to get you out of the house and you can live cost-free during that time.
You may feel a moral obligation to the bank. I would not feel this way. The banks and bankers took a ton of money out of selling mortgages to buyers and then selling securities based on the mortgages to investors. They looted the whole system and pushed prices up greatly in the process, which burned most home buyers and home owners. It's all about business -my advice is to act like a business does and minimize your costs. The bank should have required a big enough downpayment to cover their risk. If they did not, then they are to blame for any loss they incur. This is the most basic rule of finance.