Tex Murphy Series, it's actually 5 games not 3, pardon my insolence :D

*Crosses fingers*


-Darklands
-King of Dragon Pass
-Majesty (Available on GG DRM-free and modified for higher resolutions and modern PCs)

If you would be willing to include games where you must decide how the story goes, I would recommend King of Dragon Pass.

System Shock 2
Gabriel Knight
Phantasmagoria

on the top of my head: alpha protocol. Underrated and missed by many!

Alan wake: cool story if you like stephen king novels.

Max payne 3: I didn't think i would like this new max but it completely blew me away in bullet time ;)

Great Expectations the FPS

Okay that was stupid.

1: Albion
2: Gray Matter
3: Mafia


Ugh, limiting myself to 3 was not all that easy, in particular when trying to think of games that are not overly hard to find, and that on the other hand won't be recommended far too many times.
Also, avoid Limbo of the Lost.

Some good suggestions already, but my favourite is missing:

Ultima 7 - story driven, great dialogue, alive NPCs, witty companions and an enchanting world.

Or if you have played that, get Dungeon Siege 1 and install the Ultima 5 Lazarus mod. And Ultima 6 Project.
(forget about the base game though. DS1 can't hold a candle to these awesome total conversions)

The new Shadowrun seems to be fairly story driven..

Also Fable, where you get to mold not only your character appearance, but also his story (not story heavy, but a good sense of progression through it)..

and Max Payne, one of the few good shooters with also a good story..

Mass Effect
Kotor
Mafia


Thanks for the chance! ;)

Anachronox
Sanitarium
Outcast

The Last Express. A real time adventure game aboard the last Orient Express before the war. You will face characters and factions that will lead to the first world war.


Also I would like to recomend Legacy of Kain series.

The Cat Lady
Reperfection
Walking dead

- Pathologic (it'll blow your mind if you get to the end, believe me)
- Sanitarium
- Fahrenheit/Indigo Prophecy

Since some people already suggested Sanitarium - you should definitely play it - and Indigo Prophecy isn't much of a hidden gem, like you requested, here are my two back-ups:

- In Cold Blood
- Primordia

I don't really care if I win (though it would be nice!), but you should really check out these games. If you enjoy at least one of them, you'd have made my day.

(Also, all my suggestions are available here on GOG)

[EDIT] Replaced Nox with In Cold Blood. Nox does have a cool story (3 different, overlapping branches of one story, actually), but it's hardly story-driven... it's more about the action and the gameplay. So... there you go: In Cold Blood.