Google Fonts’ Raleway is one of the cleanest in the library, and is available in more styles than you’ll ever find use for. The wide weight variety makes Raleway excellent for both heading and body copy. The only downside to this font is the love-it-or-hate-it “W”.
Mrs Eaves is a Typekit font that is also available in small caps and petite caps, with an italic style that is so elegant yet so laid back that you’ll find it quite versatile for a range of different looks.
One of my newer favorites, Dosis is a contemporary sans serif font that is great for acheiving a particular modern look. The rounded edges and narrow width that characterize Dosis make it rather unique, which is rare for fonts.
Hands down my favorite serif font available through Google because of its classiness. You can’t show me a free font that elevates some guy with a small canoe to looking like a member of a global yacht club as well as Playfair Display.
Available through Typekit (free with Adobe CC), Futura is a font I compare to a nice piece of mid-century modern furniture. Rich heritage that dates way back, yet still manages to look modern and almost futuristic. Casual and artsy all at once.