We're not sure what exactly non-combat skills are to be yet - we've got some confirmation on lockpicking, and some interesting talk about the new mechanics. Likewise, we have indication of non-combat skills being usable to avoid combat, and some information of non-combat and combat skills not relying on the same resource. I've always been a big fan of skill checks for unusual things, be it in dialog, mini-text adventures, or in obvious ways. Obsidian, from all of their games I've seen, has always been pretty innovative in this - whether it be the usefullness of appraise and survival in Storm of Zehir, or the various dialog checks in Fallout: New Vegas, not to mention some of the stuff in their infinity engine work.
That said, I figured it would be interesting to find out which non-combat or more-than-combat skills everyone prefers. Clearly, D&D's skill selection lends itself to this sort of listing, but Dragon Age:Origins even had lockpicking/pickpocket and such. Clearly, these are things we'd probably also like to see in Project Eternity, but I think we can all agree they should be the ultimate judge of what skills and what uses thereof to include - despite a fondness for basketweaving.
So generally: Intimidate - I like to talk people into things, and myself out of them sometimes, but prefer the "mind your own business or else, that's why" reasoning.
Aside from that, the general "thieving" skills, though I admit a bias to pickpocket, and I lament how many games implement it as a fairly useless skill. The last really decent use for pickpocket was skyrim, and before that was New Vegas. (I imagine the gamebryo engine is a bit more suited for pickpocket/stealth systems). Taking into consideration PnP games, I'd have to say Use Rope is pretty high up, as well as climbing.