Looking for games that have a lot of this. My definition for damage-over-time is you inflict it and then it periodically does damage on its own for some time. Can be any genre.

I see you're a man of culture as well. Damage-over-time attacks, especially if they that stack through some planning, is the most fun there is to be had in games.

South Park: Stick of Truth has DoT as a mechanic, you can stack bleed, gross, fire and so on and create synergies. Fun for the whole family.

Epistory weirdly enough. You can use 'fire words' to set words on fire so that they (meaning the monsters associated with the word) slowly burn away.

In Shadowrun turn-based games there are spells that cause damage over time, and items that heal damage over time.

I recently played through Bastion and noticed that some weapons had this option when you upgrade them (meaning you can choose to upgrade the weapon to do damage over time or choose some other upgrade).

I wouldn't say it's a lot though. Not all weapons have the option, only a couple.

Pretty much every RPG has some kind of bleeding/poison/whatever attack that does damage over time. A lot of more tactical CRPG style games (Baldur's Gate, etc.) use this a lot, since buffing your character and debuffing the enemies is a core gameplay mechanic, especially on higher difficulties.

For other genres... Halo's needle gun springs to mind. Not necessarily a draining attack, but you have to land several shots on an enemy and then wait a while for them to activate and kill the enemy. Deus Ex has poison darts, both for killing and knocking people out, which will act much faster with a headshot, which is cool.

I've played quite a few RPGs where they either don't exist, exist but are not something the player has access to, or exist but are not a viable option.

For example:
* Ultima series hasn't had viable damage over time options as far as I've played. Same with Bard's Tale and Might and Magic. You have poison in some of these games, but it often isn't available to the player.
* Wizardry 1-5 have poison, but it isn't something you have access to (except in Wizardry 4, but even then you don't have control over its use).
* Dragon Quest has none, and while Dragon Quest 2 introduces poison (as an attack enemies use against you), it isn't player usable until Dragon Quest 5, and even then anything you'd want to use it on is likely to be immune.
* Final Fantasy series has poison, but it isn't a viable option until Final Fantasy 6 (it does decent damage to high HP enemies in FF4 and FF5, except that such enemies tend to be immune, even in FF5 where bosses often have status ailment vulnerabilities).
* Neither Dragon Wars nor Wasteland has damage over time effects (not counting disease in Wasteland, which again is not something you can use).

In Disciples 2 there are units that can do, for example, poison or frost damage with each turn.

Risk of Rain has a lot of this.

As I tend to mention Avernum has three major classes of DOT; poison, acid, and Disease.

Shadow Warrior 2 is all about customizing all your weapons with various properties, including setting enemies on fire, poisoning them etc. You can totally ignore the damage-over-time upgrades, or go all in on them if you feel like it.

Oh right, I knew we talked about this before. Might've summarised findings from previous time.

DoT are not interesting enough in Jrpgs, the regular fights don't last long enough and in general, bosses are immune to most side effects a weapon/spells can have.

There are a few cases of DoT in the Heroes of Might and Magic series. I'm assuming other turned base strategy games would have some as well.

Beside Crpgs, the best and most enjoyable damage over time that you can find are in mmos. Stacking up different DoTs on an enemy is a lot of fun.

Yeah, most games that have it kinda half-ass it, it's never meant as a primary source of damage. Seems the best genres for what I'm looking for are hardcore class-based roguelikes and ARPGs with liberal customization options. It's almost impossible to find a shooter or action game that has plentiful options, let alone a specialization. Even action-roguelikes with tons of weapons such as Enter the Gungeon never give you one to start out with, there's no guarantee you'll find any on your run, and even if you do it'll be with limited ammo. Only exception I know of is the Loki character in Ziggurat. Is there a specific class that specializes in it? Floramancer?

Oh right, there's the Acrid class. Unfortunately it has to be unlocked first by playing others. Wish I knew how to cheat for it.