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Categories and Subcategories of Muktzeh
There are two general categories of Muktzeh: 1) items which are useless (absolute Muktzeh) and 2) items that are used for a prohibited purpose (partial Muktzeh). Items in the first category are generally useless or may not be used at all on Shabbat. That being the case, items that are absolutely Muktzeh are prohibited from being moved for any purpose. On the other hand, items are usually not used but are sometimes used are in the second category. Items that are partially Muktzeh may be moved if the item itself is needed or its place is needed. 
There are a number of subcategories within each category that shall be explained below. Additionally, there are whole subcategories that are in doubt. Some consider them to be absolutely Muktzeh and others consider them to be partially Muktzeh. Finally, there are items that aren't Muktzeh at all.
How Muktzeh Can Be Moved
Subcategories of Absolute Muktzeh
- Muktzeh Machmat Gufo (Useless Items)
- Muktzeh Machmat Chisaron Kis (Delicate items)
- Shivrei Kelim (Broken or one time use items)
- Muktzeh Machmat Mitzvato (Items Designated for a Mitzvah)
- Muktzeh Machmat Isur (Migo DeItzkasay, Items That Were Set Aside during Ben HaShemashot)
- Bosis (A Base To Hold Muktzeh)
- Nolad (Items That Came into Existence on Shabbat)
Subcategories of Partial Muktzeh
Subcategories that are in doubt Disputed items
- Kli SheKol Melachto LeIssur (Items Used Entirely for a Prohibited Activity)
- Cooking pot
- Balls and games
Subcategories that aren't Muktzeh at all
- The Weekly Halacha Discussion (vol 2 pg 335) breaks up Muktzeh into two general categories, severe Muktzeh and light Muktzeh. Rav Hershel Schachter in a shiur on yutorah.org entitled "Hilchos Muktze" (min 16-9) explained that there's two categories within Muktzeh. One is a set of items that are completely Muktzeh (Muktzeh Gamur) and one is a set of items that may not be moved because of a prohibited use (Isur Tiltul).