It depends, I have many times liked a cover without knowing it is one, and when I heard the original, it takes a while before I like it too.
I am not against them, I think it is good, so long it is a cover and not plagiarism or taking a part of it into a completely different song.
I don't have favourites but well...
"I think we're alone now" I hear it nowadays with a girl, I knew it by "Inspection 12", I have the feeling it is a cover. Speaking of Inspection 12 "You can call me All" is another cover I like from them.
Hmm. I admit, I like some Erasure's covers. Not all, but many of them.
Specially their Abba covers, I also like covers of Erasure songs, like "siren's song" .
But I am so happy of the old songs I've learn like Abba, Bob Dylan, etc that I know the lyrics and rhythm because of the covers I'd listen too, being able to sing with your parents or friends, feels so good. specially with parents/family because it closes magically the generation gap for the minutes the song last.
Another kind of covers I like is orchestral lyric-less versions of songs. X3
Like Guns and Roses, Iron Maiden, and others.
I'll get videos later, you too feel free to share yours.