Did your ancestors come from Europe – in particular Ireland or Scotland? 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.
If Your Ancestors Came from Ireland
Huge numbers of Irish people left Ireland in the mid-nineteenth century when famine forced many people to look for a new and better life in another country. When you're trying to locate records, it's vital that you know as much as possible: if you can establish which town or village your ancestors came from, you'll know which government – whether Northern Ireland (Ulster) or the Republic of Ireland – now holds the records.