Common Words:
* Bandage
* Bandmaster
* Bandstand
Less Common/More Specialized:
* Bandwagon
* Bandbox
* Bandleader
* Bandwidth (a computer term)
* Banding (a process of classifying things into groups)
Figurative/Slang:
* Band-aid (a quick, superficial fix)
* Band of brothers (a group of close comrades)
* Band together (to join forces)
Let me know if you'd like to explore any of these in more detail, or if you have a specific type of compound word in mind!