You may have an ancestor that was born before birth certificates were issued. In some cases you may not even know the parents names, only your ancestor and his descendents. How do you locate their birth information?
One of the easiest places to start is the census records. Especially starting in the latter part of the 19th century. His or her place of birth was asked for and the citizen would give the state where he or she was born. That gives you a start.
Look for military records, even if they didn't serve. Sometimes they had to register whether they ever served or not. This is true in American history, no matter the time period. Land records is another place, believe it or not. Sometimes birth and death records had to be included in order for land to transfer.
For the 20th century, once the Social Security system was established, the Social Security Death Index will give a death date, although not always complete. It all depends on the informer. Some occur before 1960, but most appear 1960 or later.
If you find the buriel place, the tombstone, or cemetery office may have the information. Church buriel records can be another source to check out.
Once death certificates are available, they can provide, as a secondary source, the date and location of the person's birth. But from there you need to find the birth certificate, or baptismal record for a primary source. See if you can locate an obituary as this too can provide the birth information (as well as varying amounts of family information). This is not just for the 20th Century. Obituaries were printed back into the 1800's and occasionally before. In small communities, where there is little news to report, they will list birth announcements. This isn't necessarily the case in big cities. But it wouldn't hurt to look.
When all else fails, always be on the lookout. You never know where the info may pop up. Whatever you do, keep a running log of where you have looked. Over time you will forget what you've checked and you don't want to have to repeat a search only to discover you have already done that. (Believe me - voice of experience.) :-)
Happy Ghost Busting!