VR Soccer '96, not that I plan to ever play it.

Chess. I've never learned it proper.

Tex Murphy: Mean Streets + Martian Memorandum - Dec 17th, 2009

i dont plan to play that ever either
but akalabeth is the oldest i got
dont think anything will top that

Searching for a way to buy Arcanum: of Steamworks and Magicka Obscura was what caused me to discover GOG.

I bought the game on the 3rd of June 2010 and it's still on my backlog, sitting there waiting for me to continue playing together with MIght and Magic VI (26 nov. 2010), Planescape Torment (15 dec. 20210 and The Witcher (17 May 2010). All games I have already started up at some time, but have to really get going yet.

Oldest finished games are Baldur's Gate and Baldur's Gate II from the 17th of May 2011. Though they were finished before buying them here, the difference being consequent campaigns got played DRM-free instead of with a disk-checked 4-in-1 box set.

Haha, looks like I answered this on page 3. Old thread, you tricked me! At least I answered with the same game, so I'm consistent.

Answered it before, but it's interesting to see how my answer changed. :)

I'm assuming that 'backlog' refers to games I haven't finished and want to play.

The first games I bought on GOG were (I'll ignore the freebies):
Fallout
TOCA Race Driver 3
Descent 3 _ Mercenary
Sacrifice
The Longest Journey

The first four I'm not planning to play, so The Longest Journey it is. Bought 19th March 2010. (That was also my answer in the past.)

Looking at my library, most of the games I have on GOG I'm not planning to play.

As for my total library, I still plan to finish The Dig some day and play Full Throttle. I think I bought them in 1996, but I'm not sure, could have been a little later. I have The Dig installed on my tablet and got quite far into it, but I guess I didn't find it interesting enough to continue. I need to get back to it.

(That's different than my answer in the past, but I think I didn't consider what I really wanted to play then.)

Fallout
Over the years I've probably started it 30-40 times but never finished it. I absolutely love the game, I just always seem to get side-tacked by another project.

Icewind Dale, although with that said I've hardly started any of the others

Redneck Rampage

I know Tauto (and maybe others) have been on a "pointless thread necromancy" tear, but how come there are four deleted posts (90-93) ?

On-topic (since I apparently never posted in this when it was still fresh):
It depends. ;)
If you just take HereForTheBeer's qualification at face value, then the games that have been in my GOG library the longest without my having so much as tried them are: Beneath a Steel Sky, Tyrian 2000, Dragonsphere, Ultima IV: Quest of the Avatar, Worlds of Ultima: The Savage Empire, and Warsow. All were free registration gifts that got automatically added to every new account back then.
The oldest untried games I actively added to my account would be from slightly later that same day (4 July 2014): Lure of the Temptress, Teenagent, Ultima Worlds of Adventure 2: Martian Dreams, and Stargunner. Each of these was (and is) another permanently free game I found in the catalog, and I figured, "It's free, why not get it?"
The oldest game that I paid money for, but never (truly) played, is The Nations - Gold Edition, which I got only because it was being removed from the catalog at the time, and I figured, "It's $1.49, and it'll soon be unavailable to purchase here, so why not get it?" But when I eventually installed it, I couldn't get it to run properly, and, after futzing around with it a little bit, I pretty much gave up in a fit of "meh". After it languished on my desktop for a while, I finally uninstalled it, having never actually played so much as the tutorial.
The oldest game that I paid money for, and that I've never so much as tried to install, let alone play, is Planescape: Torment. I wasn't able to get into Baldur's Gate, nor Neverwinter Nights, nor The Temple of Elemental Evil, so I don't have great hopes that this will be much more up my alley when I eventually try it...but we'll see.

Then again, if you only count games that I intend to at least try at some point, you could safely ignore all those Ultima titles, Dragonsphere, Lure, Teenagent, and Stargunner (and, at this point, maybe The Nations, as well). ; )

If you wanna count video games I own outside of GOG, the oldest unplayed one I can think of would be Star Wars: Dark Forces. I got it in probably 1996, maybe even '95, but I never got it to run correctly (i.e., with sound and music playing). I sure did enjoy the one-level demo version that I played, though. =D

EDITED for formattin' fixin'.

Oldest game I own and haven't played is probably Beneath a Steel Sky.

Hitman: Blood Money.

And who says necro's are a pain?