Games to get your girlfriend into gaming

Hog games worked for mine. Nightmares from the deep and so on.
She also much liked L.A. Noire.

My girlfriend likes Bastion, Plants vs zombies, Trine 2, Roller coaster tycoon, Transister and Deponia.

I think those are fine games to get into gaming :)

Oh and the SIMS ofcourse!

Play LEGO games together, they games arent that story focused so you can just run around kick ass and collect LEGO pieces with her

3 words: Life Is Strange.

Rocket league, cities skylines and xcom :D

Tales from the Borderlands! Stardew Valley!

Maybe "To the Moon". Simply beautiful game.

Dark Souls. Seriously. See this :)

counter strike global offensive , splinter cell series :)

Binding of Isaac or Risk of Rain.

toki tori 2, eets munchies, viva pinata: trouble in paradise, dark souls

Each person is different in what type of games they like, whether it's women or men.
Your girlfriend might not like the same games you do.
My lady enjoys 2D brawlers like MK, Street Fighter, Tekken, etc.

my #1 favorite game on steam is Don't Starve! my bf let me tried it on his steam a couple of years ago and have been playing it since. really enjoy playing stardew valley atm

Add to the list Dark Souls

My girlfriend loves Castle Crashers! Highly recommended.

Bastion

Girl here!
Well, I really like strategy games, visual novels, RPGs, horror... (not a big fan of FPS because I feel sick when I play those games)

I'd recommend: Plague Inc. Evolved (nothing is more romantic than killing the whole world together! ♥), Plants vs Zombies, Long Live The Queen, Rocket League, Age of Mythology. =)

Mario obviously! :P
Hmmm, off the top of my head I'd probably say:

Giana Sisters: Twisted Dreams- It's colorful, has a great soundtrack and has rather simple gameplay (trust me, it's nowhere near as hard as people seem to think it is);
Bastion- Colorful, nice story, standard hack and slash stuff. Nothing too complicated (unless you go for 100%, then it gets quite a bit complicated).
Half-Life, Half-Life 2 and its episodes- These work really well as an introduction to the FPS genre (or at least they did for me). Honestly, I think they're really easy and if you go a step further and play them on Easy difficulty I'd expect anyone to be able to beat them (except maybe my mom).
Same thing goes for the Serious Sam games on easier difficulties. Heck they even have a difficulty called "Tourist" in which you'd have to be trying to die in order for that to happen. XD
Might & Magic: Clash of Heroes- it's a turn-based puzzle-ish game. It might sound complicated, but it really isn't. Has a nice cute short story.
100% Orange Juice- this one is multiplayer but you can play it solo with bots just fine... it's a board game with dice. That's as simple as it gets.
Castle Crashers- very basic hack-and-slash. Also an co-op! ;)
Portal and Portal 2.

Looking at the list you mentioned, I'm not so sure about Terraria... It gets pretty complicated pretty fast. And since you asked for games that aren't "dark/scary/bloody" I should mention that the very first boss you face in that games is a giant floating eyeball that has a mouth hidden under the iris.

Castle Crashers is great fun especially if you join up with another couple so that there are 4 players.

Tales from the Borderlands is the game to choose if she doesn't want dark/scary but you still want to introduce her to Telltale games.

Hatred

Yandere Simulator

You kind of really need to have played games a crap ton as a child in order to be into gaming. I honestly cannot imagine someone who has never played video games before to get into gaming. Perfect Example: My best friend never played video games as a child because his mom was afraid it was a bad influence, now he is an adult and still never plays video games.

No man's sky , Firewatchor something atmospheric....