FamilySearch.org databases are free & are added to regularly.

I use www.deathindexes.com a lot to see what's online. The site tells what's available, whether it's free, or whether it requires a fee to use. On that site, at the bottom there is a link that says "genealogy resources." Click that to find links to online births and marriages.

RootsWeb sites do not charge; neither to GenWeb sites for whatever county or state you're researching. (Just type in "(name of state)" + "GenWeb".)

Don't overlook free databases available through your local library. Some libraries offer obit or newspaper indexes; Ancestry.com Library Edition; ProQuest or Heritage Quest.

Also, investigate genealogy societies. Some societies or genealogy libraries include the use of databases as a perk of membership, or they are available for a really low fee.