Yes, there are some free sites. Just as on Ancestry.com, years covered may be limited. Many times this is not under Ancestry's control, but under the governmental entity that controls access to the record.
You don't say where you are located. FamilySearch.org is the biggest free site. RootsWeb is free. It's now run by Ancestry, but anything posted there is still free to access.
If you're in the US, check the GenWeb sites for the states or counties you're researching. Just Google "GenWeb" + (whatever state or county you want). Some GenWeb sites have a great deal of information; other sites have comparatively little.
If you're in the US, see if your local library provides Ancestry Library Edition, Heritage Quest or other databases. If so, it's free and all you need is a library card. Or see if a library in the area you're researching has any online databases that you can access.www.deathindexes.com
lists all the US states and tells what online death records exist on a state or county level. The site tells you if it's free or fee-based. A link near the bottom of that site says "Genealogy Records and Resources." That leads to links of other types of online records. Again, the site tells if the link is fee-based.