Known Knowns - done for the clear effect, which is audible by everyone (as popularised, but not invented by Cher, T-Pain, etc).
Known Unknowns - ones where most people wouldn't notice, but if you've listened to autotune a lot you'd swear it's been done (sustained notes with vibrato added seem to be clear contenders here to me, such as one in 'Angels' by Robbie Williams
Unknown Unknowns - There are lots of recordings I've worked on for people (mixing, mostly) where the vocal sounds perfect, and it's actually been autotuned/processed. Subtly, but still processed. I only know this because the person who's done it has confirmed it. In the context of a mix there's little evidence, if any at all. And if you listen to backing vocals of the last decade versus BVs from say 30 years ago, you really hear the difference - not because modern ones necessarily sound like they've been worked on, but because the old ones sound just a little bit out of tune in comparison.
I've done work on singers' recordings where I've fixed the pitch and they haven't even noticed it on their own voice, in isolation (which really is the sound everyone knows best). If done well (and appropriately), it doesn't turn it into awful processed rubbish, it can tweak an otherwise brilliant performance and make it near-perfect. I say this as a recording engineer who loves the sound of a band playing together, and would always sacrifice separation / absolute recording quality for the communication and feel that you get with a live band playing together how they normally do - I wouldn't sacrifice personality for pitch, but I think you can improve on nearly everyone's performance in some places.
Having said that, the flip side of this is that people think 'they can fix that in the mix' when they've not given a great performance... and that's never the case!