I imagine we all had to learn some poetry by heart at some stage of our early schooldays. It was demanded of us more as 'educational discipline' than for the love of poetry itself.
The first poem that I remember learning was Thomas Hood's 'I remember, I remember'.
As a smallish boy, I rather liked the poem, and managed to remember it quite easily, although I think I only managed to learn three verses (as below). I ignored the final verse.
The other one I remember learning was Lewis Carroll's 'Some Hallucinations', but again I don't think I learned all of it.
I think I could still just about recite it today.