Can I install 16GB RAM on quad-core MacBook Pro?

According to Apple the answer is no, but OWC has tested it and found that there are no issues putting 16GB (2x8GB) in the latest generation MacBook Pro. The upgrade doesn't come cheap, though - at this time 2x8GB modules will set you back $1599.

http://eshop.macsales.com/item/Other%20World%20Computing/1333DDR3S16P/

Yes. Currently $180 from NewEgg. I just installed a Corsair 16GB matched pair (2x8GB 1333MHz DDR3 CL9) on an Early 2011 13" MacBook Pro (i7 2.7GHz). Running Great! Corsair part number CMSO16GX3M2A1333C9. NewEgg link: http://www.newegg.ca/Product/Product.aspx?Item=N82E16820233217

BTW - Mid 2010 MacBook Pro models will NOT boot with this 2x8GB memory. (they will boot with 8GB (2x4GB) 1333MHz memory but see it as 1067MHz).

(No, it has two slots and a maximum of 8 GB (Apple page). Perhaps you are thinking of the desktop i7 which has 3 or 6 slots, for a maximum of 12 or 24 GB. I checked newegg, there aren't 8 GB DDR-3 SO DIMMs.

Newegg.com lists 8GB sticks. You could buy two and get a 16GB setup.