Games to train a non-gamer with?

[BoxCutter]

Dwarf Fortress.

 

[Cazza]

Start from the start with N64 Goldeneye. Goldeneye is great for teaching tactics and how to aim with a bad aiming system. Then move to Halo or a similar game. That will allow them to get the feel of easy aiming and tactics. Finally move to something like rainbow6. To iron out their flaws.

 

[Weaver]

The best way to get good at games is to run a gamut of historically significant titles starting from (most accessibly) the NES up to present day.

 

[SL33TBL1ND]

S.T.A.L.K.E.R. Shadow Of Chernobyl master mode... if she can make it past this she can beat anything...

Or tie her to a chair and force her to reach level 20 in Morrowind.

Once she figures out how to spam major skills you would know she's ready.

 

[Amnestic]

But try a wide variety of genres. Platformers, Puzzles, RPG's, shooters... and not just First-person, but also 'Mech or Flight Sims like Armored Core or Ace Combat. Let her find out what she likes.

Okay, first? Loving the avatar. Nice to see more SRW/T fans around.

Second, as far as mech-games go I wouldn't recommend Armored Core to start with. All the parts and whatnot could be more than a little overwhelming and unless she's got a guiding hand to lean her in the right direction, it has the potential to turn her off the genre entirely.

Zone of the Enders (1+2) for the PS2 are probably a better choice in that they're fairly simple, have an intuitive control system and are a joy to watch. I started with the AC series at a young age with Master of the Arena and had help when learning it, but an adult might feel patronised or controlled if you try to lean on them with parts choices.