Has any mmo game every come up with a successful method of stopping bots?

I've only played one other mmo, so my experience isn't very wide. In that one (WoW) there have been outbreaks of botting (I recall the misery of trying to farm herbs in Shalozar Basin back in the LK days with the bots farming them around you) but I don't recall they did it in any particularly 'magical' way as happens in ESO - if there was any underground or flying bots I can't recall seeing them. It was simply bots running around from node to node. And there was no sitting over a node as it constantly respawned (I guess WoW structures its nodes differently).

There used to be a lot of ore farming done by gold farmers in the previous expansion; I could recognise those as they had nonsense names, basic mounts and gear and weren't in a guild. Not so much of that during the current expansion though it does still happen now and then. Of course, its very difficult to bot farm in high level WoW if you aren't the appropriate level. You can't swim or fly to it the current highest level zone and can't use the portals until you've done the level 85 quests. That makes it a bit of work for gold farmers who have to level a toon to 85 to even get into the area (unless you have someone warlock portal you there, but you tend to die rather quickly if you are too far under 85.)

And the only time I've come up against levelling bots is in dungeons, and not very frequently of late. Is that because WoW is better at combatting it, or just that I don't see it?

While ESO doesn't have the same geographic layout style (continents divided by huge oceans that can only be travelled across using a 'public transport' system) I think the same sort of restrictions could be applied. If you made it impossible to physically enter a zone level if you are below a certain level, with quests that gave some sort of 'door key' which were quests only available to certain levels, that would keep bots out of zones until they put in enough work to allow them in. Maybe with a quest where you have to enter a typed word or words to verify you are a real person, as is done for security when signing into certain sites. And certainly put a limit on the number or frequency of new characters on an account. One a day sounds fair to me.

Im not sure how the multi-botting in dungeons could be handled, I'm not a software specialist but surely if a script can be written, it can be prevented from working. I recall the gold sellers in wow came up with a unique method of getting around chat advertising; they created a bunch of level 1 toons, sent them to the main ciities and lay them down on the ground to spell out a website address. It was frequently done for a while, and then suddenly stopped and I haven't seen it since. I'm presuming the software people figured a way to stop it, but wouldn't know how. If they can do that, then ESO should be able to handle the bot issues they are having.