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.
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.)
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.
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.
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.