The world's largest collection of genealogical records is held by the LDS Church in Salt Lake City. The LDS is currently rolling out a new search engine, with greater access to records than before. The "old" search was conducted on the IGI - the International Genealogical Index. The IGI was a massive compilation of transcribed and indexed parish records from all over the world. Parish records include baptisms, marriages, and burials (although there are far fewer of the latter indexed in the IGI). The LDS has microfilmed many but not all of the parish records in England from 1538 onwards up until civil registration in 1937, with the post-1837 records receiving more scattered coverage. The IGI also includes "member-submitted" records, which meant that individual church members could also send in their own data - however these records are notoriously unreliable. The IGI is gradually being replaced by a new, enhanced search engine that covers more records than those on the IGI - we'll deal with the new search in a minute.
To search the IGI, you will need both first name and last name of the person you are looking for. You also need to know the general area (county will do). You can get around the necessity of having to enter first and last names by including the batch number. The batch number refers to the identity of a set of records; for example, a set of marriage records from a specific parish in a specific time period has a batch number that identifies it. Fortunately, you don't need to look up the batch numbers - there is a very useful tool developed by Hugh Wallis that allows you to select the parish, time period, and type of record you want to search - you then type in just the surname and get everyone's records with that surname in that place at that time. Go here to see links to batch numbers for all of the British Isles and Canada and the USA. To search for records of parishes in England, go here.
The IGI is a wonderful resource, and if you are lucky enough to be searching for a place that is well-covered, you should find several generations of ancestors.
I said earlier that the IGI is being slowly replaced by a new search engine. To learn more about this change, see this article on the FamilySearch blog. Many people find the new search much more difficult to use. I don't know if the LDS intends to remove the IGI - hopefully not. I recommend you try the new search and see for yourself how you like it. The main advantage to the new search is that it includes more records. When you use it, pay attention to the location and the type of records you are looking for - if not, you will think you are searching for records in England and then will wonder why it is returning results in Texas or New Jersey.
The LDS is currently in the midst of a massive effort to recruit people to index original records - you download the images to your computer, index them using an online form and then send them back. There is a wide variety of records available to index: census, parish records, civil registrations, and others. Last year volunteers indexed 185 million records. This will all be available to search for free using the new search engine. I have been a volunteer indexer, and it is quite interesting to read the old original records. It also contributes to the vast resource that the LDS provides for free.