you can import a project into another project. this way all the assets (images, footage, solids, audio) will come with it.
i would select the comp (in the project window) that you want to move to another project, then choose file>reduce project. this will remove all items that are not needed for that comp (it will keep any nested comps). then save that as a new project.
open the project that you want to bring that comp into and choose file>import>file and select the project you just saved. it will then bring in that comp and all associated assets.
you may also want to check out carl larsen's tutorial for further file management tips:
http://library.creativecow.net/articles/larsen_carl/filemanagement/video-tu...
Kevin Camp
Senior Designer
KCPQ, KMYQ & KRCW