Are good introductory/pedagogical problems in algebraic geometry rare?

I highly recommend Fultons book "Algebraic curves" It's available on his webpage It's a very good introduction, and in the first chapter there are 54 exercises.

I'd also recommend Fulton's book "Algebraic curves". I recently used the first few chapters to teach an intro course to algebraic geometry and the students tended to like it. Two other good intro books might be Karen E. Smith's "An Invitation to Algebraic Geometry", or Harris's "Algebraic Geometry: A First Course".

Eisenbud & Harris' book "The Geometry of Schemes" & Ravi Vakil's lecture notes both have some good problems in them.