I went into my family tree, they gave me a bunch of bananas.
The answer (I think) you are looking for is:
Ancestry.com
There are several other sources of info for family lineage etc. Some deal with census reports in the UK and similar documents and these generally (I think) go back to around 1800 when the first census's took place. I was once told that if you can go back before 1800 with you family name, then you have a good chance of going much further. Somerset House is a good source of data. http://www.vitalcertificates.co.uk/
The main problems for certain families are that if you have a Jewish background, then because of the problems in Europe during the 2nd world war, many Jewish people changed their names for obvious reasons. If otherwise (for example) you belonged to a family in Wales, your family may have objected to an English imposed census and many changed their names to a Welsh version of 'Joe Bloggs' which was the name 'Jenkins' and if you have that name, it may be impossible to trace your geneaology.
My daughter has drawn up our family tree and has been the one in our family who has the most interest but I've only got involved on the fringes of it. She used Ancestry.com mainly plus info from older members of the family.