Let's hear em!
Combining Typefaces, A Pocket Guide http://www.fivesimplesteps.com/products/combining-typefaces
Serif: Merriweather Sans Serif: Gentona
Would love a list of resources people go to for pairings (ie, JustMyType).
One of my favortie combo of serif/sans-serif Lato (from google font) & Minion Pro (from Typekit)
Poly & Open Sans is a lovely combination.
Bembo and DIN!
I'm not sure if I can say I have a favorite combo, for me it changes with the seasons. =)
At the moment I'm working on a design where I'm using Futura Round and Elena with a dash of Guilder.
I would recommend checking out H&F-J for beautiful combo's. At the bottom every font page they show possible combinations.
For a client project, I've been using Tisa Pro and LFT Etica. It's my current favorite combo.
Jubilat & Soleil (Both are available on typekit)
I know it's cliche, but I love Adelle and Proxima Nova Soft.
I stumbled upon Raleway and Freight Text Pro when building my new site. Thought it would be funny to combine transportation-named fonts. It turns out they look incredible together.
Trade Gothic + New Century Schoolbook (especially in italics)
Serif: Lancelot Sans: Source Sans Pro