Some people have criticized modern first person shooters for having regenerating health, but there's another genre where regenerating health has been prevalent and standard since the beginning: roguelikes. Even the original Rogue had regenerating health! Nearly every other roguelike I am familiar with, including, for example, the Mystery Dungeon series (including Shiren the Wanderer), has regenerating health.

In fact, the only roguelike I can think of that does not appear to have regenerating health is Tangledeep, which is a modern entry in the genre.

So, in roguelikes, do you think regenerating health is a good thing, or a bad thing?

Depends.

Within reason. For example, fully fed I'd give regen to a player.

Yay, but not for free. You should pay for it in some way. By eating food, wasting a turn or become vulnerable.

Nope. I prefer not to have regenerating health in games, although sometimes it is demanded by the game's mechanics.
I like roguelikes with realistic combat/injury systems like Unreal World or Dwarf Fortress, where wounds take days to heal and require long term treatment.

To me regenerating health is part and parcel of roguelikes, and quite necessary in most.

However I do prefer that it have consequences. I love ToME but because it doesn't have a hunger mechanic there is basically no cost to resting so if you get in trouble you can run away and hide and rest till you're fully healed.
So each floor or each individual battle becomes its own section instead of you having to consider your route through an entire dungeon carefully.

ADOM however has both hunger and background corruption. The longer you spend in game the higher the background corruption becomes and the greater chance of becoming mutated. So you can rest, but you'd better have enough food not to starve and if you constantly have to stop to rest then you risk being hit by the higher corruption levels later in the game.

If you don't have any kind of regenerating health then you need to maintain stocks of health potions (which in most roguelikes you're not guaranteed to find) or return to inns or wherever you heal, and this can be annoying.

Or there's some other form of healing, like recovering a few hit points every time you kill an enemy. (Rogue Legacy, while not a roguelike in the usual sense, is like this once you get certain pieces of equipment.)

I don't have great reflexes, so I'm in favor of anything that makes games easier including regenerating health (as long as they don't make the screen go all desaturated or red when you're hurt).

Really though, I like the option to choose. If possible, I'd turn on regenerating health AND health packs.

The thing is, your "don't have great reflexes" issue doesn't matter when it comes to roguelikes, as they're turn based; if you don't give the game any input, nothing will happen. No enemy will try to attack you while you are trying to decide what to do, no enemy will get you before you get to enter a command, and (if present) health regen will not occur either if you don't give the game any input. You have all the time in the world to tell the game what you want to do.

In fact, years ago I looked at a few games being played on a public NetHack server, and there were games where a player would go AFK (Away From Keyboard) for a while; when you come back, the game will be just as you left it.

(By the way, immediate pick-up healing items (like health packs) are not common in true roguelikes; I heard that they exist in DoomRL, but they're generally not something you would expect to find.)

Route, I presume you are on your mobile with auto-correction (may it burn in hell) on.

I am fine with it as long as it is not as ridiculously fast as in Call of Duty.

How about the (rather simple) approach taken by Shiren the Wanderer (and many other Mystery Dungeon games):
* If your belly is not empty, you recover some of your health (about 1/150th of your max; I think this is the number Shiren uses) each turn.
* If your belly is empty, you instead lose health at that rate.
* Even a minor food item (like an herb) will give you 5 belly (enough for 50 turns), so using them when you've taken damage from hunger (rather than using them the instant you start starving) can be a way to conserve food.

(The situation could be interesting in something like Pokemon Mystery Dungeon, if say you have no food but do happen to know Leech Life, which you can use to keep yourself alive if you can find an enemy to use it on.)

From what I've read, The Flame in the Flood is described as "rogue-like", but the game mechanic doesn't use "health" per-se, rather a combination of hunger, thirst, temperature and fatigue. All rechargeable, but constantly draining as you go on. This particular game currently has my interest peaked atm.

If it makes sense to auto-heal, why not? But if it is happening for no reason but to make the game easier for the player and seems overtly unrealistic, then maybe it isn't a good idea.

The industry likes to misuse words for marketing purposes. From looking at the screenshots, it doesn't look like a roguelike. Similarly, stuff like Binding of Isaac, FTL etc are no roguelikes either. It's nice that some people moved away from this and now call those games roguelites. Sure, it's still not accurate but at least it provides some distinction.
As for the question of whether regenerating health is good or bad...it always depends on how it's implemented. I'm more familiar with regenerating health but I certainly don't mind the other option if it works decently.

Aren't rouge-likes supposed to emphasize perma-death? Regenerating Health seems to take away that tension of scraping along if you're just going to Wolverine it while waiting.

It's like Alien Isolation, what made that fun was the physical save locations and the potential loss of progress that made all actions all the more tenser and suspenseful. Auto save ruins that and so does unlimited manual save.

The most direct meaning of the term "roguelike" is like Rogue. Since Rogue has health regeneration, a game that has health regen is more like Rogue than an otherwise similar game that does not.

Also, maybe you should try playing Rogue: even with health regen, the game is not exactly easy.

(It might be interesting to actually compare Rogue to various definitions of the term "roguelike" like the Berlin Interpretation; it might be interesting what aspects of the definition Rogue fails to satisfy.)