It really depends on what country you are interested in.
FamilySearch is probably the best general site, with a huge amount of records from all over the world. although some of their sources have restrictions such that you can only access them at a Family Hustory a Center, but they would still be free.
In the UK, there are sites like the Online Parish Clerks.
A few US states have free access to vital records.
The French Archives are free, and have both civil and church records.
For Dutch records: Wie Was Wie.
For Austria records, Matricula, which also includes some German and other records.
The Czech Regional Archives.
Many US public libraries have subscriptions to sites such as Ancestry that you can access for free through the library websites. A library card is required; some libraries have free remote access.
FamilySearch has free access to a number off subscription sites, Ancestry among others, but these must be used at a FHC, although church members have access to some.
There is generally no free access to modern records.