Kasper, the theme that I am using for this web site, comes with three fonts: Open Sans, Merriweather, and Inconsolata. I did not like these very much, so I set out to find suitable replacements.

For the moment I settled on Fira Sans for headlines, Charter for body text, and Source Code Pro for code listings. These are the only free fonts recommended by Butterick's Practical Typography. Charter is a serif typeface and was originally designed for late 1980s printers. It performs quite well on modern displays, retina and non-retina alike. I am indebted to Matthew Butterick for packaging Charter as a web font. Fira Sans was designed in 2013 by Erik Spiekermann et al. for Firefox OS. Source Code Pro is a community project initiated by Adobe. Fira Sans and Source Code Pro can be used through Google's web font service free of charge (barring some privacy concerns).

Incidentally, all three fonts can be used in a LaTeX document:

\usepackage[T1]{fontenc}
\usepackage{charter}
\usepackage[charter]{mathdesign}
\usepackage{sourcecodepro}
\usepackage[lf]{FiraSans}