Normal chakra is the type of chakra we see during most of the show, it has a light blue colour to it. This chakra is sort of a LVL.1 chakra. It can be used for most skills, but you need a lot of it if you want to perform higher level ninjutsu.
Healing chakra is the kind of chakra medical specialist like Tsunade, Sakura and Shizune use for healing-purposes. It's a light green chakra that can heal physical damage on one's body. All we know is that it heals wounds at an accelerated rate, we do not know if every shinobi has, and can mold this type of chakra. It seems that the user focuses this type of chakra to their hands, and then touches the injured spot to begin the healing process. It's unkown if this chakra is actully used for skills.
Kyubi's chakra is a special type of chakra that can only be used by Naruto, and of course the Kyubi itself. Naruto can use this chakra because of the demon fox that was sealed inside him. He calls upon it in times of great emotional excitement, and later on Jiraiya learns Naruto on how to control it. The chakra has a redish colour. And it's a far more powerfull type of basic chakra, it is used to perform high level skills which requires a tremendous amount of chakra. When Naruto let's a part of the Nine-Tail's power leak out, the seal that sealed the Kyubi appears on his stomach.
This chakra can only be used when being marked by Orochimaru's cursed seal. (Being bitten by Orochimaru, and having survived the 10% survival-chance.) It's a dangerous type of chakra. And if it's used too much, it will drain the hummanity from a person, and the user becomes a slave to Orochimaru. This Chakra is dark purple one, and becomes active when the user is out of his regular chakra. Visible black shapes will appear on the body and the user will be given a tremendous amount of evil chakra power.
By opening chakra gates (releases the body's limits on muscle usage/chakra flow) your body and muscles will be put on a lot of strain. Altough your attack will be a nearly suicidal attack, you will be able to perform continuous speed and high powered attacks, making this highly devastating to any opponent. This is the chakra Lee and Gai use to perform their lotus-attacks. Apparantly this is a deadly type of chakra that is best used by people advanced (strong) enough in Taijutsu, hopefully being able to bear the heavy strain placed on your whole body. Someone can open up to 8 Chakra gates, some of the user's chakra will turn green and surround him. By opening more chakra gates, your granted power will increase. But in most cases the result is immobility of the user, due to torn muscle fibers.