Thousand of freeware fonts are available today. Here are some which are actually recommendable in the category “serif”. They have a sufficient number of styles, a sufficient (Latin) character set and an acceptable stylistic and technical quality.
A free serif font family in 12 styles by Friedrich Althausen.
Alegreya is a typeface originally intended for literature. Designed by Juan Pablo del Peral for Huerta Tipográfica.
Bona Nova is a new version of the old-style italic typeface Bona, originally created in 1971 by the Polish designer Andrzej Heidrich, known for his design of Polish stamps and banknotes.
Designed by TypeTogether for the Google Play Books app.
Cormorant is a free display type family developed by Christian Thalmann. The project currently comprises a total of 45 font files spanning 9 different visual styles (Roman, Italic, Infant, Infant Italic, Garamond, Garamond Italic, Upright Cursive, Small Caps, and Unicase) and 5 weights (Light, Regular, Medium, SemiBold, and Bold.)
PT Serif was developed for the project "Public Types of the Russian Federation." The second family of the project, PT Sans, is also freely available.
Source Serif Pro is a set of OpenType fonts to complement the Source Sans Pro family.
The serif family of the IBM Plex super family.
Charis SIL is a Unicode-based font family that supports the wide range of languages that use the Latin and Cyrillic scripts. It is specially designed to make long texts pleasant and easy to read, even in less than ideal reproduction and display environments.
The serif family within the Noto superfamily. A display version is also available.
Cardo is a large Unicode font specifically designed for the needs of classicists, Biblical scholars, medievalists, and linguists. Since it may be used to prepare materials for publication, it also contains features that are required for high-quality typography, such as ligatures, text figures (also known as old style numerals), true small capitals and a variety of punctuation and space characters.
A free font family originally developed for the Mexican book store chain Gandhi.
Merriweather was designed to be a text face that is pleasant to read on screens. The Merriweather project is led by Sorkin Type, a type design foundry based in Western Massachaussets, USA
Gentium is a typeface family designed to enable the diverse ethnic groups around the world who use the Latin, Cyrillic and Greek scripts to produce readable, high-quality publications. It supports a wide range of Latin- and Cyrillic-based alphabets.