From what I've gathered and witnessed over the years theres two main schools of reasoning:

1) the old "oh those things are useless, get a REAL gpu!" elitism - where a dev, dev team, producer etc may simply not want to support and have coded in something to prevent the game from running (Fallout 3 requires using a custom exe in many cases because the game detects an intel and simply wont run).
This somewhat continues today with the "not supported" on system specs. Some indie devs are geting pretty bad for it (ive even seen some belittle people on steam discussions and spew elitist gobshitery). Some come round though when they realise that at lower resolutions, you dont need 500 different effects running, and things have come a long way in the last 10 - 15 years.

2) Sponsorship. I dont think its as common now, but back when games on disc were common, the distribution was often sponsored by a GPU manufacturer. With a good deal of games that had certain companies logos flash up at the start and "intel gpus not supported on the back" in an age of increasing DRM, it would make corporate sense.
If i were at liberty to talk openly about it, the best i could supply is anecdotal evidence from friends that worked at some big companies at the time, but for me its enough.

I might be rambling a bit there. Hopefully you get me though.

I just have a Pentium G3440, using its integrated graphics. Admittedly, what can be played on it is greatly aided by my trusty 13 y/o 1280x1024 monitor, so the GPU doesn't need to do full HD or who knows what.

Anyway, had this for almost 5 years now. During that time, the more demanding games I played were Tropico 4 (medium settings I think, getting choppy when things got crowded, but was manageable), Gone Home (really low FPS, felt like it was often even below 10, but not like it's a problem in that game), Torchlight (no problems), Driftmoon (can't really remember whether it was a bit slow at times or not), Ember (struggling at times, but manageable), Jotun (fine), Lords of Xulima (no issues when traveling, choppy in battles with many enemies, especially when there are effects as well, but not like it's a problem), Venetica (has choppy moments, when there are effects and camera moves quickly mainly, but manageable) and Ascension to the Throne (can get really sluggish, but can deal with it with this type of game).

PS: You can also say I'm running it crippled, since I had the setting to allow extra power to GPU when needed disabled all along, so it sticks to the power budget for the CPU package, takes CPU all the way down to 800 MHz when GPU is taxed badly and does what it can like that, so even this very weak integrated GPU could work better if allowed.

I had a similar thread here.

I'll update it later this week, mainly for other Intel users to check.

Assuming a game uses OpenGL (couldn't find the equivalent documentation for DirectX, but it's likely there):

The game could call getGlString(GL_VENDOR), which returns a string like "NVIDIA" or "INTEL" (or "ATI Technologies", though I don't know if that string is still used by modern AMD GPUs), check the result, and if it returns "INTEL", refuse to run. Or it could just check for the 2 major graphics card vendors, and if it doesn't match either, refuse to run (this would also make the game not run under software rendering).

Of course, a simple check like that is relatively easy to patch out, if one has access to a good binary debugger and is skilled with the use of such things; the hardest part is locating the check. While doing this to get rid of copy protection can be difficult, as programmers go out of their way to make things difficult, doing this to change something unrelated to copy protection is not going to be that hard. (With that said, this assumes the binary isn't encrypted as a whole, in which case one would need to decrypt the binary, change the relevant part, and either re-encrypt it so that the game is satisfied or also remove the call to the code that tries to decrypt it.)

The newest game I played on Intel graphics was the original Risen and that was stuttery. I tended to stick to point and click adventures.

I can understand gaming on an old laptop but if you have a desk top for the love of god do yourself a favour and pick up a cheap GPU

Or get a cheap Ryzen PC because the onboard graphics let you comfortably play any modern game at 720p

I play on laptop: I have no desktop PC and do not plan to buy one. I'm going to buy laptop with better specs and dedicated GPU, but I'm delaying the decision on purpose. There are just still a lot of old games I have a lot of fun with and actually I don't feel the urgent need to upgrade. Considering the genres I prefer, there are still some relatively new titles I can easily run and enjoy on my hardware - and still I've got a huge backlog of even more appealing classics. Sound like a good reason not to hurry ;)

One of the newer games I've played and enjoyed is Vaporum. I think it's perfectly optimized, I had no issues and I was really impressed how it looked. For me 2-5 years after release a game is still quite new :D

The best way to increase the performance of any Intel GPU is to beat them in pieces with a hammer.

Are they still far behind AMD's APU's
I mean i have an old i3 (Running at 5ghz :) ) , but I've always considered it only useful as a chromebook in how powerful it is.
Are you suggesting that there are games that i would actually want to play on something so under powered? do tell!

Pył (Dust) would be a good example, a hybrid of Windows and DOSbox that was unplayable until some russian fans made some magic with the engine, otherwise there was no way to make it playable.
And it was really demanding game at release too.
https://www.mobygames.com/game/py

If you want to let people know what can be played with Intel HD graphics, please mention also the CPU name as different CPU's may have substantial diference in graphics performance!

Any integrated Graphic solution can be improved quite substancially by running the RAM in dual channel mode (2 sticks instead of a single one). I've seen 50% improvement in some games but 20 to 30% is more the norm.
If you have a computer with one 1 stick of ram, buy another one (even if they don't match exactly in size). DDR3 and DDR4 are very forgiving using 2 un-matched sticks in dual channel mode.

Before Intel HD 4000 series (Sandy Bridge stuff) there were a lot of compatibility problems with Intel integrated graphics, however there are some games developed specifically for them, like Grid Autosport.

Off the top of my head, I could name hundreds of the many thousands of games that work on Intel laptop iGPU's including:-

+ Virtually every DOS / ScummVM game ever written
+ Most 90's games
+ Many 2000's games
+ Some modern lightweight games
+ A very large percentage of the point & click adventure, 2D platformer, isometric RPG & puzzle game genres

Doom 1-2, Divine Divinity, Darkside Detective, Diablo, Don't Starve, Deus Ex, Dex, Dragonsphere, Dangerous Dave, Downfall, Day of the Tentacle, Don't Escape 4 Days to Survive, Desperados, Driftmoon, Daggerfall, Defender's Quest, DROD 1-5, Dark Fall, Deponia, The Dig, etc, are barely a fraction of just those starting with letter "D", excluding all other letters (and all other games not on GOG, eg, Dune, Discworld, etc), that should run well on low-end laptops, so you can see how big a "list of games that run on Intel iGPU's" could get.

If you're serious about maintaining such a list, this topic sounds like it deserves a properly maintained Google Sheets spreadsheet linked to in post 1 rather than people just randomly dump games over dozens of pages to avoid the topic just "fizzling out" as many do without an easily accessible structured list. You could have three columns like "Name of Game", "iGPU" (because an Intel Iris Pro is not an Intel HD 2000) and "Tweaks Required" (eg, 'disable anti-aliasing', 'needs DX11', 'needs HD4000 or newer', etc) that will allow details of what tweaks are required to run without disrupting a one game per line format. Kind of like how the "2nd class citizen" thread works. If you then grant permission to edit it to some trusted people here, the workload could be spread over several people making it more likely it will be kept updated without the one person who originally created it getting "burned out" on maintaining such a huge list.

Some games that run ok in most Intel HD (tested on Cherry Trail Z8350 Atom) graphics are:

Into the Breach - Plays great with touch screen!!!!
Guacamelee - 960x540 res and 60 fps. BoomChacalaca!!!!!
Broforce - Sometimes a little lag during major explosions
Mark of the Ninja
Limbo
Shadowrun Returns - a little laggy but playable
SkullGirls - Playable
Grid - (also known as Race Driver Grid) playable but not at 60fps.
Richard Burns Rally - plays nice with a little lag here and there
Live for Speed - not 60 fos but doable

Will add a couple more when at home.

All these games should be playable on most laptop and every desktop integrated Graphics after HD 3000. The z8350 is the lowest end CPU on the market and is very weak, most games are limited by the slow quad core itself.

I have an Intel HD 2000.

I can play Darkest Dungeon with minor graphic glitches every once in a while, have completed the game without problems. Crimson Court and Color of Madness expansions are unplayable (they work only partially, can't be played fully).

All of these work perfectly fine: Baldur's Gate 1 and 2 enhanced Edition, Icewind Dale EE, Planescape Torment EE, Torment Tides of Numenera and Pillars of Eternity (haven't tried the sequel).

All the LucasArts adventure games originals, remakes and and special editions work fine, except Grim Fandango which won't run with this graphic card. Thimbleweed Park works great too.

The Shadowrun games work great.

These won't work:
Star Wars Knights of the old republic 2 (the first one works mostly fine, I've completed it without incident)
Divinity: Original Sin - Enhanced Edition :(

Not relevant to me at the moment, but back when I ran lots of games on an Intel HD laptop, I achieved that with:

1. Install the latest Intel HD graphics drivers. (This fixed e.g. Empire Earth for me completely.)

2. Install the game.

3. Play the game.

Naturally for newer games Intel HD graphics may not have enough power, but if you are talking about backwards compatibility with older games, my experiences back then were quite positive (as long as I had updated the graphics drivers). I could even run Gorky 17 flawlessly, while on my NVidia Geforce the game had massive graphics glitches, making the game unplayable. (Nowadays Gorky 17 has apparently been fixed to run on modern GPUs so I presume those issues don't exist anymore on the GOG version).

It's worth noting that your GPU appears to be of the generation before DirectX 11 support appeared, and as such will have issues that the HD 4000 and later will not have.

(Putting this comment here for context; this post is certainly useful for those who are still using those older GPUs, but not as relevant for those with newer ones. Sometimes, recent low-spec hardware can run certain games that older high-spec hardware can not. Divintty: Original Sin - Enhanced Edition is an example of a game that requires DirectX 11 or OpenGL 4.0.)