Which card has the highest number of mana symbols in its mana cost?
Progenitus has 10.  This is easy to check in gatherer, just use CMC >= 10, and see that it's the max.

Draco has the largest generic mana number, at 16.  (Observed using the same query.)

If you include unsets (I know you didn't want that, but for completeness, and because I love them) Big Furry Monster from Unglued has 15.  And Gleemax has generic mana requirement of 1,000,000.