Styles drop-down menu does not work on posts or pages: the type size does not change. Changing headings doesn't change anything, in Visual Editor or in HTML.
These are w ways to change fonts on wordpress.com blogs.
(1) Changing font families, colors and size in text in posts or pages either post by post or page by page by coding into the HTML editor. http://en.support.wordpress.com/editors/font-size-color/
(2) Changing font colors in text in posts or pages either post by post or page by page using the #4 icon (Select text color – change the text color) in Row 2 the Visual editor. http://en.support.wordpress.com/visual-editor/#row-2
(3) Changing all font families, colors and sizes throughout the whole blog by purchasing an annually renewable Custom Design upgrade and using Typekit Fonts with Staff support. http://en.support.wordpress.com/custom-design/
Note: Any font changes to font families, colors and size in the blog title, tagline, post titles, page titles, categories and tags cannot be done without CSS editing.
Do you have CSS editing experience and have you purchased an annually renewable a custom design upgrade?
If not then you can only use (1) & (2) above. If you have been unsuccessful doing either of those within posts and pages you could have a browser issue. If that's the case please try clearing your browser cache and cookies. If your browser version is out of date you can upgrade any browser version here.