Common words:
* quick
* queen
* quiet
* quilt
* quiz
* quote
Less common words:
* quack
* quaint
* quarrel
* quest
* quiche
* quiver
* quoit
* quorum
* quixotic
* quibble
* queue
Proper nouns:
* Quentin
* Quaker
* Quebec
* Quetzalcoatl
Other:
* quantum
* quadruped
* questionnaire
This is just a small sample, as there are many words that start with "qu." Do you have any specific categories in mind? For example, are you looking for words related to a particular theme, or words of a specific length?