I need some inspiration; what are some good examples of systems that use 2 six sided dice as their core mechanic, in any way whatsoever.
That's how the original and extremely simple Tri-Stat d6 works. In order to succeed in any given check, a player must roll equal to or less than the relevant Stat (Body, Mind, Soul, or an average value based on several Stats) on 2d6, with possible difficulty modifiers adjusting the result (from -4 for "Trivial" to +6 for "Practically Impossible"). A natural 2 always counts as a success and a natural 12 as a failure; otherwise the difference between the result and the target number determines the degree of how well the character performs (from exceeding the TN by more than 8 for "Critical Failure" to falling below it by more than 8 for "Critical Success").
PIG's GDi games - Hard Nova ][, Coyote Trail, Colonial Record, etc.
Classic Traveller
StarBlazer Adventures (one is a plus die, the other a minus die)
-clash
Traveller is pretty interesting, especially how it has (mostly) held up in the Mongoose iteration a lot of its original form.
Truth & Justice (and other Atomic Sock Monkey "PDQ" games), uses a 2d6 system as well. IIt is basically roll 2d6 and add a ranked trait and beat target number. It shares quite a bit with Traveller (such as damage to "attributes") but the similarity is only vague. In Truth & Justice setbacks tied to traits trigger future possible plot events tied to a trait. Traveller is just "losing points" from the attribute temporarily, which kind of makes some sense, since you are weakened and made clumsy by wounds impairing your actions.
As above BESM used a roll under mechanic which used 2d6, and the target numbers were modified based on how difficult something was when you attempted an action.
I'm not coming up with any others right now--I think because the games I own are either D20 powered (literally not the general D&D term)--such as Talislanta, Hellas, or Waste World; or use d10's a lot. With a few oddities that use cards, or some other varient system (like Spirit of the Centuries fudge dice, or D6's pools.)
Look at me! Look at me!
See sig.
Tunnels & Trolls uses 2d6, with doubles giving an extra roll, for everything except hand-to-hand fighting.
IIRC, In Nomine, while considered 3d6 (or d666), is effectively just a 2d6 roll w/ the third die being a "check digit" for how well the feat was accomplished (also allowing for rolls of 111 (the trinity), or 666 (# of the beast) which cause other game results).
There's also Battletech if you're looking for some combat ideas using a 2d6 system. I can't remember how much the Mechwarrior RPG add-on used d6s... Maybe other remember.
Uh, lessee...there's also Marcus Rowland's Forgotten Futures, and Allen Varney's Toon. Um...those are the only other ones I can think of off the top of my head.
The sample game system that Gary Gygax designs in his book Master of the Game uses 2d6 as a base.
If I'm remembering right, Fighting Fantasy uses 2D6.
Decipher's CODA sytem for 'Lord of the Rings' and 'Star Trek'.
Gee, I have that LUG TOS game, too...I shoulda thought of it.
I had to register just so I could post about one of my favorite games.
Conspiracy X first edition, I hear the second edition uses Unisystem, I only looked at the character sheet and figured it not worth getting.
The system compares your stat with a difficulty number to return a target number, starting at 7 when they are equal, +3 or -3 for each difference along with any other modifiers. The idea is to get the target number the highest so you can roll under with 2d6.