Y-DNA will track back via a father's surname, male-to-male-to-male, until and unless there's a "non-marital event" that breaks the chain. However, in the case of mtDNA -- mitochondrial DNA, which tracks maternal lineage -- the surname will change with each generation (unless the mother's maiden surname was the same as her married name). So whether mtDNA can be of any assistance depends on what you're trying to trace. It won't help you very much, if at all, with the traditional, routine genealogical task of tracking a surname back through time.
Autosomal DNA -- atDNA -- is helpful going back about five or six generations, but (as I understand it) past that point it's not particularly reliable.
I'll leave it to others more expert than myself to offer more detailed comments.