Fonts like Open Sans, Droid Sans and Roboto are only preinstalled if you're using an Android device and there are many other fonts that aren't preinstalled, so how can you use them? "If a page uses web fonts, then the font files have to be downloaded to the site visitor's computer before they can be displayed initially. The font files are served compressed for a faster download. After that initial download, they will be cached in the browser. As the Google Fonts API becomes widely used, your visitors will be likely to already have the font you're using in their browser cache when they visit your page," explains Google.
A search for fonts.googleapis.com in Chrome's cache page (chrome://cache/) returned font families like Open Sans, Tangerine, Oswald, Noto Serif, IM Fell English, Arvo, Droid Sans.
If you want to download some of these fonts to your computer and sync them when they're updated, you can install SkyFonts, a free software for Windows and Mac OS X. "SkyFonts automatically updates the fonts installed on your system whenever they are updated on Google Fonts – for example, when new characters are added – ensuring you always have the latest fonts to work with. And with the fonts installed locally, browsing websites that use web fonts will be faster, since your browser won't have to spend time fetching font data," mentions Raziel Alvarez, from the Google Fonts team.
There are 624 font families and 1105 fonts right now, but SkyFonts only lets you download fonts one by one. It's probably a good idea to visit the Google Fonts directory, sort font families by popularity and download some of the font styles from fonts.com.
If you don't need the syncing feature, you can also download fonts from the Google Fonts site: click "Add to Collection" next to the fonts you want to download, then click the "Download" button, download the font families in your collection as a .zip file and use these instructions.