First you should find out why the person requires a co-signer. The lender may have any assortment of reasons, the most common being bad credit. If the person looking for the loan has bad credit then they may require a co-signer, this is a good sign that maybe you should not sign. Other reasons may be that the person hasn't been at their job long enough or that they are young. These are times when it is up to you to make the call.
 You should know the person you are co-signing for well. And it is not always a good idea to co-sign for friends. They may have good intentions, but if any problems do come up it may be the end of your friendship. Family members, depending on how distant, are usually alright to sign for, if you know the reason why they need a signer. Don't volunteer to co-sign for your neighbor's step-sister's great niece twice removed, it's just not a smart move.
 Take a look at your finances. Remember that if they stop paying that you are automatically responsible for the payments. Are you financially able to make those payments if it comes down to it? If your finances aren't in the best shape, then you probably shouldn't be a co-signer.
 Note that if there are any problems with the loan that they are going to reflect on their credit and yours. If you have a good credit score it can be blemished with a co-signing that has gone bad. Make sure you feel secure in signing, you are putting your credit on the line.
 Check out the interest rate on the loan. If they are getting a bad interest rate then see if they can qualify for a better interest rate with your credit score. This will help them out, but it will also help you if it comes down to you paying it. You don't want to get stuck with a terrible interest rate for a loan that didn't even benefit you.
 Know why the person wants to take out a loan in the first place. If they need to buy a car or finance their education, then they are getting a loan for a good reason. If they just want to buy a new TV or computer, or take a vacation, then you are very justified to say no to co-signing. They will be alright if they have to wait until they can pay cash for any of those things.

Signing your name tells them that you have more faith than they do that the borrower will make on time payments and pay the loan back in full. There are some circumstances where you will know that you are ok to co-sign, but if you have any doubts then it is okay to think twice before making your decision.

Having good credit is one thing that will help you get where you need to be in life, so make sure that you don't ruin it because you wanted to be nice and help out a friend in need. You have to live with your decision.