Typography, as the art of font design, does not give us a distinct definition of modern font in its current understanding. It is rather a collective notion of the typefaces, popular these days, than some particular style or trend in font building. As a matter of fact, modern font family may include the examples of a vast variety of other font categories. Calligraphy scripts and graffiti fonts, digital typefaces and fancy dingbats, and many other separate types can be found here, among modern fonts.
On the other hand, in typefaces classification we can still find a description of a traditional modern font. This modern typeface dates back to the beginning of the 19th century and it, actually, has nothing to do with digital fonts, we all use today. By that slightly outdated definition, modern font is characterized by the strong vertical stress, high contrast between the thick and thin elements of letters, and serifs. Times New Roman is, perhaps, the closest example to illustrate such modern font.
However, if you try searching the web for modern font examples, you are likely to be directed to really immense number of fonts with the recent dates of development as, perhaps, the only similar trait. In regard of font anatomy, modern fonts include all the variety of typefaces: regular, bold, italic, outlined, with vertical stress and with no distinct stress at all, with and without serifs, and with a variety of stylish embellishments.
Just to give a few examples of modern fonts, let us mention such typefaces, as Elevation, Rosie, Infrared, Public Gothic Federal, and Oceania Display. Basically, the free modern font collection, available at Fonts2u, includes over two thousand different typefaces, related to modern trends in font design. Of course, the more options we have - the higher chances of finding the necessary font are. And with Fonts2u, one can be sure that he will get a really impressive range of options to choose among.