proxima nova is hot right now
Open Sans, very versatile, looks good on all the browsers and it's free.
Current favourite combo is Montserrat for headings and Freight Text for body (serif). It's got personality but doesn't draw undue attention to itself.
I like Museo font a lot.
Circe is nice
Montserrat, Proxima Nova, Open Sans, Dosis...
I love using Apercu in web:
I'd go with Montserrat as well, but keep in mind it's pretty limited when it comes to different font weights from Google Fonts. I usually play it safe and use Raleway as it comes with so many weights. Only downside is no italics - but who needs em?! https://www.google.com/fonts/specimen/Raleway
We use this font on one of my biggest clients website in regards to UX as it is so legible and pairs very well with many Serif fonts. Try looking into Domine, Poly, or Enriqueta as great pairs. All on Google Fonts as well.
roboto is always working well for me
Proxima Nova is my favorite.
I think one of the best Google font is open sans. Very readable. Droid Serif is also good.
Recently I'm using often Google's Roboto, the font of Android 5 UI.
Din Next coupled with FF Tisa is a nice combo I like.
i prefer arial for every website. such a classic look!
Oswald is a very nice google font.