I counted my GOG games today, I have 125.

Then, I said "how many of these are truly classics that are essential? How many of these would I REALLY miss if they went away? How many of these are a genuine part of my life and my history? How many would I feel emotional about if I could never play them again?"

I counted 13.

13 out of 125 is about 10%.

Figure out your essential percentage! List the games if you want, here are mine:

7th Guest
Arcanum
Arx Fatalis
Chronicles of Riddick
Fallout
Fallout 2
Under a Killing Moon
Deus Ex
Deus Ex Invisible War
Thief 2
Thief: Deadly Shadows
The Witcher
The Witcher 2

How many are essential parts of my life, games that have shaped my way of viewing games and that I also own on GOG? Very few. I'm buying the games that I don't already own here, so I lack the nostalgic ties that a lot of people have to their games in their libraries. Out of the ones I own here:
The Last Express (CD was going bad). One of the most beautiful and interesting adventure games ever, and one that helped shape my love for adventure games.
Ultima Underworld 2: I loved exploring the world in this game as a kid. I still do.
Beneath a Steel Sky: Another one of those "important" adventure games
Fallout: One of the earlier "heavy" CRPGs that I played, and one that shaped my love for CRPGs in general.
Legend of Grimrock: The game that got me interested in tile-based FP CRPGs (I have since got my hands on Eye of the Beholder 1-3, and played through 1-2)
King of Dragon Pass: I just love the way this game builds stories as you play it.

How many of my GOGs would I really miss if they went away?
Realms of Arkania 1-3
Resonance
The Last Express
Ultima Underworld 1-2
King of Dragon Pass
Little Big Adventure 1-2
Beneath a Steel Sky
Legend of Grimrock
Freespace 1-2
Fallout
Master of Magic


This list would be a lot bigger if I were to list games that I own physical copies of though.

I just did the math. I have 172 games. After sorting through the list, I whittled it down to 35 I'd fit into your listed criteria. That's 20.35%. There are plenty of others I'd be sad to see disappear, but that's because I haven't had a chance to play them yet.

Here are my 35 games:
Another World: 15th Anniversary Edition
Beneath a Steel Sky
Cannon Fodder
Crusader: No Regret™
Crusader: No Remorse™
Descent 3 + Expansion
Descent + Descent 2
Duke Nukem 3D: Atomic Edition
Dungeon Keeper™
Dungeon Keeper™ 2
Fallout
Fallout 2
Giants: Citizen Kabuto
Gobliiins pack
Heroes of Might and Magic® 2: Gold Edition
Heroes of Might and Magic® 3: Complete Edition
Hostile Waters: Antaeus Rising
MDK
Painkiller Black Edition
Populous™
Populous™ 2: Trials of the Olympian Gods
POSTAL 2 Complete
Psychonauts
Quest for Glory 1-5
Redneck Rampage Collection
Sacrifice
Sanitarium
Settlers® 2: Gold Edition, The
Sid Meier's Alpha Centauri™
Simon the Sorcerer
Simon the Sorcerer 2
Star Control 1+2
Syndicate™
Theme Hospital
Unreal Tournament 2004 ECE

0, I guess.

I don't have a huge catalog, but essentials would be:

Beneath a Steel Sky
Broken Sword series
Tex Murphy series
Thief series
Fallout 1/2
Witcher 1/2
Dreamfall: The Longest Journey

That's kind of a strange question; I'm going to interpret it as 'which GOGs do you count amongst your all-time favourites', if you don't mind. In which case:

Fallout
Beneath a Steel Sky
Planescape: Torment
Master of Orion 2
Tyrian
Psychonauts

There are others, but I don't own GOG copies of them.

Edit: That's 6 games out of 56 = 10.71%

Better percentage than me!

I just thought it was fun to really whittle them down.

Since I only have a limited amount of time for gaming, I mostly buy essentials, therefore my percentage is rather high.

There's a subtle distinction. Under a Killing Moon is not as good a game as many others in my collection, but because if when I played it and how important it was to me at the time it is an "essential game" in my life.

Hmm... I don't know about general, but many GOG games were essential to me. I think I bought half of the games I really ejoyed or desired as a kid but were unavaible. And most of them are really important to me to this day.

The other chunk of games I bought here are games I didn't know. (i started gaming in mid 90s) and bought them because they were recommended as classics by community, for example. And most of them are amazing still.

Out of my 44 games, I would consider these essential in my library:
Fallout
Fallout 2
Fallout Tactics
Commandos Ammo Pack
Desperados
Sanitarium
HoMM III
Postal
Arcanum
Carmageddon

102 games here. X-mas sale should change that. 22 here that stick out for me are:
Might and Magic 1-9, Ultima 1-9, Master of Magic, Master of Orion 1-2 and Theme Hospital. I'm sure that there are a few I missed but it's 2:18 am in L.A.

Out of 98 games I have here, I'd rate 10 of them as "essential", as in I still replay them fairly often despite having finished them lots of time, and I'd be genuinely sad if I couldn't do that any longer. That's 10.2%.

The list:
Fallout
Fallout 2
Baldur's Gate
Baldur's Gate 2
Planescape: Torment
Arcanum
Heroes of Might and Magic 3
Master of Orion 2
Alpha Centauri
Pirates

all or none...

Thief 1-3, BG 1-2, Fallout 2, Deus Ex 1, Arcanum, Duke Nukem 3D, Longest Journey, Giants CK and maybe a few more.
It's amazing how few of my games here on GoG I've actually played. But I never view my list of unplayed games as a "pile of shame" but instead as a pile of possibilities. I just love that I have so many different games to try and for the very low prize I payed they will give me a few hours of joy and in this miserable life, what more can we expect?