Hoping to find a few games that can be played for a VERY long time -- sprawling worlds, endless modes, or radiant quests... etc.

Any ideas welcome!

Well, Arena, Daggerfall, and Skyrim all have radiant quests.

Elminage Gothic has a massive post-game, including a 20 floor dungeon at the end, one that I have not beaten because the difficulty really gets ridiculous. (There's an enemy that is very fast, can attack twice, each attack hitting 4 times for 300+ damage each time, and I hear that, later in the dungeon, there's an even more powerful version of that enemy.)

The Pokemon Johto games (Gold, Silver, Crystal, Heart Gold, Soul Silver) are famous for including a whole other region (Kanto from Generation1) in the post-game, which its eight gyms, although not as polished as the rest of the map.

Minecraft keeps getting updated to add more stuff so there's that. I don't play the game often, so I haven't even touched most of that stuff since maybe 2012.

So this must be specifically "endgame" or "endless" mode or just game for long time? Because there is plenty of sandbox type games like RimWorld, Factorio, Dwarf Fortress, Terraria etc. that can be played for hundreds hours without even touching "endgame".

Battle Brothers would qualify as well.
There's a limited number of ambitions ("Have a roster of at least 12 men", "Visit every town and fortification in the world", "Accumulate 2,000 gold for a battle standard", etc) and random world map events/encounters getting thrown your way, but the mercenary contracts (the "bread and butter") periodically generated for each settlement should be infinite.

I'm up for any long game...

... but I do have an interest in games where you can continue playing once the initial story has completed.

I'm willing to look at anything... extension of gameplay being official (ie radiant quests, endless modes, or just really long games) or mods extending gameplay.

As I remember both Darkest Dungeon and Hand of Fate 2 had endless modes. I've had this in my backlog for quite awhile. Had been waiting to play it until I acquired the dlc... but maybe I'll give it a go sooner! Yeah, I should play more Daggerfall and Arena!

I know that the games that have given me the most amount of enjoyable playtime are Fallout 3 and New Vegas, especially if you include mods.

This was my first thought too (New Vegas is my GOAT game and I'm always praising it) but when playing without an "endless" type mod, the end of the main quest in both Fallout 3 and New Vegas is the end of the playthrough. Certainly, one could try to experience as much as possible beforehand and take hundreds of hours doing so before the point of no return, but technically there isn't "post-game" content. One could start a new playthrough with a different build or do different questlines, so Fallout 3 and New Vegas are eminently replayable, just not in the sense of "post-game" or "new game+" style.

Since I haven't seen it mentioned, I'd offer a recommendation for Just Cause 2. To attain full completion of the map takes a long time and is something the player likely does after finishing the main campaign.

You are correct about the technicality, the title references post-game content but the question seemed to just be about game content in general to which I think we both agree the Fallouts qualify. If we want games with content after the main campaign specifically then my first thought would be the Arkham games, where you usually can't even change your costume until you've beaten the main story but has a lot of additional content and new game+.

Starbound can be included to the list.
The endless mode begins right after defeating the first boss, and may go for hundreds if not thousands of hours depending on the player's mood.
And the game is made with the idea of being easily moddable to the point you don't even need mods for that! (spoiler: in-built cheats let you make vanilla-friendly modifications to the game, some quite wild) So if you count modding capacity, that's even more stuff to add up to the endless mode.

Good call, I actually must have skimmed over the OP itself as you're right it gives a different impression than the topic title does.

A couple more recommendations for OP/anyone interested:

Agarest series (from what I understand involves lot of grinding, as well as post-game content)

Dead Cells (more post-game content than initial campaign, albeit there is repetition of the biomes/levels)

The Mount & Blade games come to mind. Mind you, the first game has no overarching "main quest" at all -- it's a pure sandbox. And Warband (base game) only has a short introductory questline which can be ignored with no consequence. (I haven't played any of the others, but I gather that at least the still-in-development Bannerlord has a somewhat longer, more involved storyline to go with the usual open-world sandbox.)

The Saboteur, while not having a particularly long main story, has a handful of completely optional mission chains and a ton of open-world objectives to check off the list. Crucially, fairly few of the latter "free play" objectives are collectibles; the majority are Nazi military emplacements or equipment to be destroyed, or generals to be killed. This at least means that (most of the time) you won't feel completely taken out of the game by doing these objectives, since they're (mostly) pretty much in keeping with what a member of the French resistance (or at least the version presented in this rather "comic-booky" game) might do.

I mean, say what you will, but most Ubisoft games (Ghost Recon, Division, Farcry, Assassin's Creeds etc.) certainly do offer a ridiculous amount of content, whether that content is enjoyable or worthwhile is obviously YMMV.

Uff, plenty of options I'd say
Trying to have them in categories in no special order with few personal experiences
(but frankly they overlap very often):

*New Game+
-Infinity Blade 1,2,3 - mobile
The vgame carries the experience level & items
You go all the way up to the God king, defeat him and start over (bloodline cycle)
The end? When you decide when you are bored enough of leveling up...
Great ios vgames, a shame they were removed when Apple decided 32bits to die

-Valfaris
It has the Full Metal Mode, quoted:
"essentially a New Game+ that turns the deadly up to MAX by remixing various aspects of gameplay.
The new mode will unlock after completing the game, so if you've already got a 'Clear Game' save file,
you'll be able to jump into Full Metal Mode as soon as the update's been installed.
Here's a rundown of features:
-All weapons, upgrades, and upgrade items carry over between runs
-Enemies have increased health, attack, and aggression
-Bosses receive the same buffs - with additional attack patterns
-Therion takes more damage
-New Destroyer Class Weapon
-New Achievement for defeating Full Metal Mode"

Heard also nice, but pending to me:
-Dishonored 2
-Batman: Arkham Knight

*Huge number of combinations
-Battleheart Legacy. quoted:
"• An astounding 150+ unique skills across 12 classes to customize your character with.
Poison your foes, crush them with giant two-handed weapons, put them to sleep with a song,
or simply blow them up with a meteor strike. And with our unique multi-classing system,
it's possible to combine classes into a nearly limitless number of combinations.
• Over 200 unique pieces of equipment to further tailor your character's play style"

*Special endings / Fighting vgames
-Street Fighter 2. Beat the story without losing a single round. Did I mention it has 8 characters to master?
-Mortal Kombat Trilogy. +20 characters, special moves, fatalities, brutalities, animalities, friendships...

*Survival Mode
-Plants vs Zombies. (Don't clearly remember) Unlocked once you finish the story mode
Also has a Zen Garden to waste as much time as wanted

*Collectibles / 100% completion
-GTA3, GTAVC. After/While finishing the story, lots of time needed to finish:
side missions (phone, vehicles, rampages, gangs), find the packages, perform the unique jumps...
Big part of mastering those vgames happens there

*Sports / versus: FIFA, NBA, NFL (career, tournament, versus. Many teams/roasters to choose)

*MMOs:
-World of Warcraft: The story mode alone falls short to all it can offer

*Re-visit long time ago played vgames