Nice Question! I'll give it a shot w/o my notes...
Well, we have Prenatal/Preheaven/Congenital Qi, and Postnatal/Postheaven/Acquired Qi, for starters...
Prenatal Qi is the Qi you are born with. Postnatal Qi is the Qi you get from the environment around you. So a baby's first breath is its first taste of postnatal Qi.
The main type of prenatal Qi is Yuan-Source Qi, which has both a warming and activating function, and essentially relates to the original function of organic systems. It is formed through the dynamic relationship of Yuan Yin and Yuan Yang at/in MingMen. From there, Yuan Qi flows through the San Jiao and into the other meridians, pooling at the Yuan Source points of the various channels.
The two main types of postnatal Qi are Kong Qi (air Qi) and Gu Qi (food/valley Qi.)
Kong Qi is breathed in by the lungs, which absorb the Qing Qi (clear Qi) from the air and excrete the turbid air Qi (I forget what this is in pinyin.)
Gu Qi is absorbed from food and water (and the senses, imo.) The stomach rots and ripens the food and sends the clear Qi of the food to the spleen, where it is transformed into Gu Qi.
The Gu Qi from the spleen is sent to the chest where it mixes with the Qing Qi absorbed by the lungs from the air, forming Zong Qi (Chest/Gathering/Ancestral Qi.)
Through the actions of Yuan Qi, the Zong Qi transforms into Zhen Qi as it leaves the chest. Zhen Qi in turn is comprised of two relatively opposing aspects: Wei Qi (defensive Qi) and Ying Qi (nutritive Qi.) Wei Qi relates to the entire spectrum of self-defense/immunity, and flows outside the channels during the day and inside the channels at night, Completing 25 cycles in the day and 25 cycles at night for a total of 50 cycles. Ying Qi relates to the entire spectrum of nourishment/repair, and cycles through the channels 100 times a day along what is commonly known as the Chinese Organ Clock.
Then we have Zheng Qi, or upright Qi, which is comprised of the Zhen Qi, Zong Qi, Gu Qi, Kong Qi, and Yuan Qi. It's a term used to describe the sum of someone's resources in contrast to a particular Xie Qi (Evil Qi.)
Then you have the various Qi of the 12 Zang Fu, such as Spleen Qi, Stomach Qi, etc.
Plus the 7 emotions are considered to be Qi as well... and there are the 5 seasonal Qi, the 6 climactic Qi... I'm probably missing some... but oh well that's my answer for now.
What's that, like 50 types of Qi?
"It is the peculiar quality of a fool to perceive the faults of others and to forget his own." -Cicero