The 'Hell No' people are ignorant. Pick any of the games mentioned in this thread (except Animal Crossing if you don't want your life sucked away), and you'll have plenty of 'series worth playing on a handheld'. As much as I respect you for being a Eureka fan, you need to open your eyes.
Generalized opinions like 'The gamecube sucks' or 'the xbox sucks' or the 'ds sucks' are plain ignorant.
Note: Definition of Ignorant before someone gets too offended:
Ignorant: Destitute of knowledge; uninstructed or uninformed; untaught; unenlightened.