You gave me opportuniy to remember about Shadow of the Horned Rat and catch it on sale, thanks !
Wil it really come soon to GoG ? it is better I think than first one regarding character creation, well, at least the visual of the characters, much more choice :) Would love to play an amazon in it !
I own Dragon's Dogma, it's a great game and manage to be a rich setting even without the Fantasy races to me.
Divine Divinity is such a great suggestion, thanks for reminding it to me !
And Sacred 1 ! So many good memories with it :) Thanks for the help ! Also I loved Dark Quest 2 but I'm not sure if it is present on GoG, if that can help you, or Divine Divinity as someone suggested it even if it's sometimes a bit parody, but not the point it prevents immersion.

That's nice, but The Temple of Elemental Evil is what I thought should've caught your eye here. It uses D&D 3.5e, has turn-based combat, sports backdrops of pastoral hamlets / dark dungeons, and it's Greyhawk to boot. Can't have it more classic than that. It's literally what you're asking for.

no idea what's DDO, but I've updated my post somewhat. Can't say more than that really.

Yes. I 2nd that. The Drakensang games

DDO is Dungeon and Dragon Online :)

Interestingly, most people look for less generic. A few that popped into my head:

Lords of Magic is very "generic fantasy". It's a dual-layer strategy game. Can be challenging.
Lands of Lore is very "generic fantasy" grid-based-first-person fantasy RPG. Eventually needs a walkthrough.
Fantasy General was already mentioned. Turn-based strategy. Can be "flat".
Dungeon Keeper is quite traditional generic fantasy strategy, except you're evil and win ("good is dumb" is quite a common trope). Dungeons takes it a little bit further, but is close enough to remaining generic fantasy.
Majesty is very "generic fantasy". It's an indirect-control real-time strategy game.

Dungeon Siege

https://www.gog.com/game/dungeon_siege_collection

Tolkien lovers btw should at least give the mordor games a go, if you did not so already ;)

warner bros did quite right with shadow of mordor and its successor, some movie references, a bit of tombraider meets assassins creed, no party of course.... never managed to make it quite far because the game is quite lengthy a i'm a bit allergic to huge open world type of stuff

another interesting game might be the Warlock of firetop mountain

Allow me to breach my hiatus from the flaming dumptruck of garbage the main forum is to momentarily peer in, and slide in a suggestion.

Avernum/Exile is slightly different. But not so different that you wouldn't find it out of place. The big weird thing you gotta consider is that most of it takes place underground. But otherwise the setting is standard Swords & Spells with an occasional Terry Pratchett style on the nose pointing out of things.

Geneforge on the otherhand is a bit wilder; with living tools and being all about creating your own dedicated monsters.

How about Two Worlds?
I haven't played it myself but what attracts me to the title is that it looks very unpretentious and generic fantasy-wise.
Just by the way, I have similar taste in "generic fantasy" so this thread is helping me out too.
Thanks for making it!

Battle for Wesnoth - free turn based fantasy strategy game: https://www.wesnoth.org/

Also has lots of add-ons if you dont like the 'mainline' campaigns/settings.

I personally enjoy Two Worlds II. Two Worlds one never did click for me, others have enjoyed it, but I thought it was pretty rough around the edges. I would say not to expect the polish that you would find in a game like Witcher 2, but I remember it being fun for what it was. It has been a while since I played it though, so I cannot really remember any particulars.

People who actually love Tolkien's books should avoid those like the plauge. If they weren't tied to the LotR license they'd be decent games, but as a tie-in to Tolkien's world they are a disgrace. Edgy, angsty power-fantasy.

Here is a pretty great article on what's wrong with Mordor's story, though I could add that even combat feels just wrong for this world.

Now that's actually a very good suggestion. I think the game is a bit frustrating with its difficulty, but then that is pretty true to its old-school mentality. And it does look wonderful as it recreates a feeling of playing a tabletop game.

My summaries of games others have mentioned and a few of my own:

Ultima series 1-8 (ignore 9) = very old rpgs with a dash of sci fi in the plot.
..... all gog accounts should have U4 free, so you can check that out.
Might and Magic 1-8 (again, ignore 9) = old rpgs with a little sci fi near the ends.
Heroes of Might and Magic = strategy games in the same MM universe, no sci fi.
..... if you only want to try one I suggest H3, as that seems to receive the most modder attention (WOG and Era), though both H2 and H3 have lots of maps.
King's Bounty = strategy games very similar to the above HOMM games.
Lords of Magic, special edition = very old version of HOMM games. Need extra software to make it playable.
Dark Messiah of might and magic = action rpg (despite name not a MM game, just Ubisoft deception)

Temple of Elemental Evil = rpg with a little planar stuff near the end.
Gothic 1 and 2 = German rpgs with only humans and orcs, highly recommend. Low magic.
Eschalon 1-3 = rpgs with a little sci fi in the plot. Walking is slow.
Neverwinter Nights 1 = long rpg with TONS of mods to choose from.
Dungeon Master = very old puzzle/dungeon crawl abandonware, precursor of Legend of Grimrock
Dungeon Crawl:Stone Soup = hack and slash roguelike, zero story. Free game, active development for over a decade.

I don't know what your tastes are so I don't necessarily recommend any of these games, I just list them as suggestions for you to look at and decide for yourself. The only one I do recommend as it seems to fit your tastes is Gothic.