Did your ancestors come from Europe - in particular England or Wales? It's quite possible to find their records. You may even be lucky enough to find records online, because as more and more people become intrigued with their origins, more are being made available.
Most genealogical resources group England and Wales together, because they were administered together. Where you go to find records depends on how far back you want to go. If you're looking for birth records after 1920, you'll probably find them at the national government level. If you want a birth record from the 18th century, you would need to look at the parish records, and those records are now held at the county level. Therefore, the more you know about where your ancestors came from, the more you will be able to focus your research.
Start your search at the Family Records Centre in London (http://www.familyrecords.gov.uk/frc/)
, which holds indices to births, marriages and deaths registered in England and Wales since July 1, 1837. You can order copies of the certificates online. The site is well laid out, and explains that if you need a document earlier than 1837, you need to search parish registers, which are very variable: http://www.familyrecords.gov.uk/topics/religious-2.htm.
Parishes once managed all local affairs -- they kept records of marriages, baptisms and burials, looked after the poor, and maintained the local roads. The parish records are now held at the various County Records Offices throughout England and Wales. Some have their own Web sites, and even provide online access to catalogs and records. Genuki at http://www.genuki.org.uk/
will help you to find the County Records Office for the county you're interested in.
Census Documents in England and Wales
Censuses were conducted in England and Wales every 10 years starting in 1801, but the early censuses, up to 1841, were purely statistical, and did not contain names. Census records are released after 100 years, and the 1901 census is online at http://www.1901census.nationalarchives.gov.uk.
This huge database contains information on 32 million individuals, along with original census pages. Access is free, but you're charged for viewing transcribed data, at 50p (around 90 cents U.S.) per individual, and then 50p for all the other people in that person's household.
The index links to digitized images of the actual returns, so if you have a large-format printer which prints A3-sized paper (which is standard in Europe), you can print them out.
Unlimited Public Records Searches - http://www.recordapro.tk/