Other techniques can be useful in breaking through brick walls as well. First, collect every piece of information that you have linked to this ancestor and analyze it again even if you think you know it all by heart. Sometimes information only becomes relevant when viewed in context with another piece of information. I was surprised at some of the things I came to realize when I actually did this myself.
Sometimes you need to forget what you know, or rather what you think you know. Unless you have documentation to back it up, the names you are searching for may not be accurate to begin with. Try going back to the last piece of documented evidence that you have and go forward again to see what new developments you might find.
Know the history of the area that you are researching in. It is possible that part of the problem may be that you are searching in one county, or state even, when in reality at that particular time the area was in another county. Find out the date that that county was formed and the parent county. Records that date back prior to the date that the county was formed most often should be searched in the parent county.
Another technique that you can use is to try researching siblings or cousins of the person in question, called collateral lines. So far this has not worked with my husband's grandmother because I have yet to prove her maiden name. However, this technique can still be utilized when this type of information is missing; just drop back a generation and research siblings. Another type of genealogy that is similar to this is called "cluster genealogy." Very often our ancestors migrated and lived in close knit groups of family and friends. Sometimes if you can find out who the neighbors are you can uncover hidden family members or even clues to your brick wall ancestor.
Many other useful and fascinating tips to uncovering your mysterious ancestors exist. Keep learning and keep reading, and most of all, don't despair. Information that you think is useless today might be the key that unlocks your mystery tomorrow.