If the person has a game controller and likes 2D platformers, you could try Shovel Knight. Note that I consider the difficulty of that game to be comparable to that of the NES Mega Man games, but it is in a genre that the person should be already familiar with. (The game is playable without a controller, but I would recommend one here.)

Transistor - good story and cool design, done. I'll try to think of a few others.

In RL, I don't think so. Well, maybe World of Goo. But in general I often recommend Steamworld Dig as a sweet indie game that's easy to pick up, addictive and not too challenging. It's also on the shorter side.

I thought of another one:

Cave Story (original freeware version) could be another good choice. The game is of moderate difficulty (you won't beat bosses on the first try, for example), but if the person is already decent at 2D platformers, this would be a good choice for your friend.

I think Portal might be nice.

Terraria is as close to a universally likeable game as possible.

Thanks for the suggestions!

You might consider my idea stupid but Pillars of Eternity is something that also caught my attraction for this matter.
It has nice visuals, an easy difficulty mode and the story is good as far as I know.

Or am I completely wrong?

You might want to consider indie games made in homage of 8-bit and 16-bit games. Have you tried Freedom Planet and Shovel Knight?

Seriously? Any AAA game from one of the big publishers! They have ingame tutorials for everything, quest markers to show you where you have to go and aren't exactly hard. Your friend played SNES? He/She's ready for modern PC gaming ;)

It is a very good choice and one the best cRPG one can find today (it's destined to be a classic like Baldur's Gate does today), just keep in mind that it requires a lot free time to enjoy (it's quite big) and i'm not taking into account it's expansions. If your friend has much free time on their hands, go for it. Should they find it too hard overall, there is the "Story Mode"** which makes things even easier.

** http://pillarsofeternity.gamepedia.com/Mode

If he's played only on consoles then he missed out on FPS, RTS, TBS and RPGs.

I'd get him Doom (the classic one). Seriously. It's THE quintessential PC game.

Also AoW:Shadow Magic, Civ4, XCOM:EW if he's interested in the TBS genre. Maybe watch a couple of let's play before deciding. I hate it. =)

So much grinding, no tutorial, no manual, not a flipping hint on how to progress unless you spend days on the wikia. This is also an excellent suggestion. Great games, quite simple but very very fun.

It's a tad big maybe for a fisrt attempt.

The shadowrun games are shorter and damn addictive. Invisible Inc is great fun. In another genre, the Gabriel Knight remake or Pirates! could be great starting points as well.

Hammerwatch

Trailer: https://www.youtube.com/watch?v=4MIWVwPydOk

A very fun hack and slash dungeon crawler with very simple controls. Very enjoyable be it in single player, co-op or multiplayer.

Its a very much underestimated game and very cheap at the moment with less then 1.75€ price.