I've seen multiple cartoons and comics where the Hulk is not green, but red. Is there any explanation for this? What are the changes to his powers and personalities? Does he have any other 'colours'?
The Bruce Banner Hulk has been portrayed as both grey and green over the years, largely due to changes in printing technologies, artist changes, etc.
In the late 80s, Marvel retconned the changes to reflect an unrevealed Dissociative Identity Disorder (DID) that Banner suffered from long before he became the Hulk. The physical effects of his Gamma radiation mutation reflected the dormant personalities that were part of Banner's psyche.
They also used the mental illness to explain why the Hulk's intelligence would vary dramatically over the course of the character's development. Peter David took the idea even further to introduce more varied personalities, like Mr. Fixit.
The Red Hulk is an entirely different character.
General Thunderbolt Ross, in an effort to finally defeat the Banner Hulk, undergoes a variation of the super-soldier program that transforms him into the Red Hulk. Part of Ross' plan involved faking his own death at the hands of Red Hulk, presumably at Banner's request, so that his true identity would remain secret. Since Ross doesn't suffer from Banner's DID, he is better able to retain his intelligence and tactical knowledge.
Later in the series, Ross uses the same process to save his daughter Betty, turning her into the Red She-Hulk.
The Red Hulk is a different character.