Be sure to protect your Social Security Card by keeping it at home in a safe location. Any documents containing your number should be stored carefully or shredded. However, no matter how careful you are with your documents, people will still occasionally ask you for it outright. If that happens, follow this sequence to protect it:
1) Ask why they need it
Don't just give it to anyone who asks. It's amazing the places that ask for it that have no use for it at all. I've even been asked for my SSN at a video rental store!
A SSN is used for social security and now, for credit reports. Some non-retailers will still ask to run credit like utility companies because they are essentially entering a credit relationship with you, but for any business that has no legitimate need of your SSN, be as firm as possible about not providing it.
Also, when applying for a job, if they ask for the SSN (which they need to pay you), tell them that you'll provide it AFTER you're hired. In some cases, a credit check is a legitimate part of the hiring process (depending on the job you apply for) in which case you will have to provide it.
2) Ask what happens if you don't provide it
If withholding your number results in not getting service, that's probably fine for some places and not for others. For example, you might need a cell phone for your job and since every cell company asks for a social, you may not have any choice. Move to step 3.
3) Ask to use an alternate ID
Most places that ask for a SSN do so only for laziness because they want some kind of identifier to distinguish you from other customers. Ask them to use an alternate ID.
4) Hold, freeze, or zero
After getting that far and if the first three options haven't helped you, you'll need to make the decision to withhold the number (despite the consequences) or to protect your SSN another way. Withholding it is pretty straightforward.
The second option is to go ahead and provide it knowing that awill protect your credit report. It's still better not to let your SSN be spread around any further than it has to so consider the next option instead.
In cases where legal and ethical to do so, you can try this trick: substitute the middle numbers of your actual social security number with 00. No legitmate SSN has any of the three fields all 0's so this is guaranteed not to belong to someone else. In case you ever have to remember the fake you used before, it's easy because it's simply your SSN with the middle two numbers removed.