Plants VS Zombies is universally considered one of the most potent gateway drugs.

edit: poll, used to. When we got together she was going through a HOG phase, but had owned consoles previously. With me she built her first gaming PC and went on to play competitively; last I'd heard she had joined a WoW clan.

don't starve together?

Depends really, everyone has their tastes. But if she hasn't ever even touched console before in her life, it might be tough. Anywho I give you some game ideas that got my gf interested, although she would never play em alone. And that is what seems to be the case with your girl too, everyone doesn't like to play alone on pc/laptop unlike on consoles or mobile handhelds. That's why Im adding coop games to the list too.

Minecraft
Portal 2
Sims 4
Europa Universalis 4 (weirdly enough)
Rollercoaster tycoon
Ibb&Obb (disliked Trine series though)

EZ, Chess.

Btw, go tell her to make me a sandwich with her extra special sauce.

Portal

From the "new" games i would recommend Undertale, Stardew Valley.
From some old games Chariot, ibb & obb and some other co-op things.
The keep talking and nobody explodes is another good co-op game.
Child of light has some ok art and story and its easy to learn and play.
Ori can be a bit difficult to some people and it's pretty good.
For some co-op building rpg game starbound is better than terraria, but terraria is fine i guess.

There's lots of games what game she may like? she only saw you play witcher 3 or you know something she like?

Most of the ones i said you can play offline.

Figure out her preferences. Something like Crashlands could be great, since it offers a nice mix of combat difficulty and challenge with relative casual pacing. But if she's not into that kind of fighting or if she can't keep up it'll frustrate her.
Also, determine how competitive she is.

My girlfriend is into gaming, but she's used to being the 'best girl in her class'. Now I've had a few years of experience on her when it comes to gaming because she didn't have a computer or console in her house from a young age and I'm better at many games. As a result she gets frustrated because she likes to be the one that is better so she can teach and assist - rather than being outshone in every department.

She has played Gnomoria to death since it allows her to play at her own pace while still offering quite some depth and complexity.
Similarly a game she's played since she was young is Wizardry 8 - again a game that allows you to pause and play at your own pace.
The common theme? Turn based games and games you can pause or slow down. Allowing her the time to think and plan.
That may be an element to keep in mind which would open up titles such as Dragon Age, similar to Witcher but without the immediate combat pressure.

It depends on the person but:

Long Live The Queen
http://store.steampowered.com/app/251990/

The Sims 3
http://store.steampowered.com/app/47890/

not a game but a social group GirlGamers
http://steamcommunity.com/groups/GirlGamers

list of games with female protagonists
http://store.steampowered.com/search/?snr=1_4_4__12&term=female+protagonist#sort_by=_ASC&tags=7208&page=1

A couple games that are good and aren't too hard for someone new to gaming:

Metroidvania types:
Dust: An Elysian Tale
Insanely Twisted Shadow Planet (slightly higher difficulty)
Guacamelee
Aquaria

FPS:
Half-Life 2
Saints Row 3 or 4 (hilarious and not too hard)

Puzzle:
Portal/Portal 2 (if she has patience as some can be downright hard to work out, but that's part of the fun)
Letter Quest: Grimm's Journey Remastered (bookworm/scrabble style RPG)
Lyne

Shooter:
Cosmochoria
Major Mayhem
Really Big Sky (You will die, lots. Get over it.)

Sim:
Always Remember Me (dating sim)
L.A. Noire

Misc:
Audiosurf 1 and 2 (easy modes)
One Finger Death Punch
Goat Simulator
Super Sanctum TD

I'm sure there will be plenty of people arguing against some of these. I'm happy to discuss them.

My ex was not into games at all. Which is why she's my ex.

I'm just messing.

Not really.

Things that dont exist- Kappa, Bigfoot, Lochness monster, Gaming Girlfriend.

Adventures! Gim Fandango, The Longest Journey, Sybeira... All three of these are AWESOME, adorable, classics and not scary at all. I'd start her off with The Longest Journey and then move on to Syberia and end with Grim (because of the skeleton-looking characters that are still not scary in the least).

Actually, the way your girlfriend will get into gaming is basically how I got (back) into gaming too. I had a boyfriend who played The Witcher 1 and I'd just lie there on the bed and watch him play. I loved it. I then went off to buy him more games that I'd like to watch him play and slowly I joined in when I saw him play Neverwinter Nights. We got into a lot of fights over whose time it was to play and over me "enjoying the ingame flirting too much" xD He was "a bit" jealous xD xD xD

I originally got into gaming on my own and did it (not counting Super Mario) with these 3 adventures + Sanitarium, but I wouldn't recommend it for her because it's dark and sometimes creepy.

Ooooh, almost forgot- make sure to introduce her to the awesome world of visual novels and HOGs :D :D :D
Ooooh and Dragon Age: Origins! Dragon Age is amazing and you get to flirt with Zevran <3 <3 <3

Also almost forgot- SKYRIM!!! Just give her the god-mode code if she prefers not dying and let her run wild :D

My wife loves WoW, Minecraft, Sims 3-4, LoL. But she also plays with me the co-op, such as Battleblock Theater, Chariot, Lovers in a Dangerous Spacetime, Magicka'n'stuff like that. She doesn't like FPS, but she played few hours of Borderlands. She would play Sims all day long. And Minecraft.

lol i was about to recommend dead space until i read "preferably ones that aren't dark/scary/bloody" its what got my wife into gaming and me more time alone to play when she is home lol, she used to scream and jump off the couch playing it but it just made her love it even more, these days she loves the fallout games as well as the elder scroll games (i got her into those because they have 100s of hours of game play lol)

Stardew seems like a lot of fun, but it really depends on what she's into. It could be that she wants to play games with you and wouldn't be too into playing single-player, but I don't really have any clue about stuff like that so don't take my word. Anyways, based on what you said she played and liked, I feel like she might like Abyss Odyssey? Or maybe she'd play something like Papo & Yo?

Puzzle games might be a good choice to get her comfortable with gaming, Critter Crunch has a really fun/funny single-player adventure and has local and online multiplayer (co-op or vs.) and has cute/bright graphics, so maybe she'd like that? It also builds up all the features at a nice pace in Adventure, so you don't get overwhelmed, but by the end you're doing all sorts of cool stuff without even realizing it's actually quite complex...
I personally really love it and actually only bought it because my sister tried and adored it and she really wanted me to get it to play (I've now played it waayyy longer than her) It also has a regular price of $7, so it's probably a cheaper alternative to some of those others?

Also Teltale Games. My sister loved the wolf among us (she isn't into gaming at all)

Shadow Puppeteer
http://store.steampowered.com/app/316480/
Never Alone (Kisima Ingitchuna)
http://store.steampowered.com/app/295790/
Divinity: Original Sin
http://store.steampowered.com/app/373420/
BattleBlock Theater
http://store.steampowered.com/app/238460/
LEGO series
http://store.steampowered.com/search/?snr=1_5_9__12&term=LEGO
Magicka
http://store.steampowered.com/app/42910/

Choice of game depense of your gf, and youre relationships.
The Best choice, i think, its Deponia
http://store.steampowered.com/app/214340/
But theres no coop. Just Point and click fun adventure.

I usually go back in the time machine for this. The games that got me into gaming and have stood the test of time like Super Mario Bros, Tetris, and Portal are what I usually use to introduce someone to gaming.
Additionally, it's nice if she can experiment to find her interest in genre. For this I go with iconic games that really revolutionized what the genre is. From what I hear, the Half Life series to be among one of these all-time greats for FPS, but I didn't experience it personally. As well as, of course, the games I listed above.

Mechanically most of the games you picked out look good. Sidescrollers like Ori and Rayman are great for learning players since they don't need to worry about the controls as much. Stardew + Rancher I guess depends on if she likes the farming genre, some people find it dull. Terraria can get a bit complex: Going into it without a guide as a new player can quickly lead to frustrating deaths or hitting dead ends; while using a guide will give spoilers and ruin the sense of adventure. Perhaps something like Minecraft is better for a newer player.

Tale of two brothers has a nice story and can be done as single-player controlling both brothers. I played it through on my own and thoroughly enjoyed it. I'm not a hardcore gamer, but I do enjoy games with a good story. Other option to maybe challenge/interest an occasional gamer: A nice tower defense game since it's straightforward to play. Plants vs Zombies?
It's difficult to tell what genre she might like.
Slime Rancher is one I'm looking forward to try myself one of these days (keeps fingers crossed) I expect it to be real good.

Life is strange

Guns of Icarus Online

I hv try BattleBlock Theater with my girlfriend, pretty fun.
She even finished the solo part while i hv only finished half.

Tekken

Assassin's Creed, my girlfriend loves it