What I think would give Nunu a more interesting kit.
Nunu and Willump
What this concept-kit tries to accomplish: More mechanical depth but retaining simplicity. Less punished by what he ranks/doesn't rank. Jungling and supporting botlane both being valid options. Retaining a thematic coherence. Makes him good at ganking lanes, being the go-to jungler-support. Can build like a Support, Fighter or Tank.
New Passive - Outrage Gains AS based on a nearby ally's or monster's missing health. The bonus AS decays when not triggered. Also gains bonus MS towards enemies when nearby allies have low health.
(Something interesting that fits well with their personalities; half animalistic rage, half defending the bullied. Speeds up the last few hits on a camp. Incentives jungling but also for him to gank bullied lanes. )
Consume (Q) Deal true damage to a non-champion and heals Nunu for a percentage of his health. Grants his passive's bonus MS for a few seconds. The first use of Consume on a big monster increases Willump's size and gives CDR for a few minutes, stacking up to a cap.
(Base functionality the same, but with standardized bonuses. Also having Health-scaling makes sense on his defensive/sustain ability. CDR feels very good on Nunu, so it's a good incentive to keep it stacked up. Lane Nunu's harass and sustain is a bit lower than Jungle Nunu's, unless he helps out a lot with objectives.)
New Blood Boil (W) Outrage's bonus AS stops decaying over the duration. Temporarily transfers a flat amount of AS to target ally and a portion of Nunu's **Outrage **bonus. For the duration that ally's attacks gives Nunu a stacking increase of Base AD for a duration. Self-cast gives the Bonus AD on hit, no AS and lower cooldown.
(Now less of a fire-and-forget bag of stats. Gives Blood Boil some optimal-use-cases and synergy with more things.)
Ice Blast (E) Damages and Slows target enemy. Damage and missile speed scales with Base AD. AP increases Damage and Slow.
(Total AD makes it scale with levels and my version of Blood Boil, allowing some more freedom in what ability to rank first. Now has some optimal use cases. Missile Speed gives a bit of flavour.)
His ult is fine as-is, imho.
What do you guys think? What would you do with Nunu's kit?