Problem: When you create or modify a webpart for a page it is only available for that page. Assume you create a list on your site and want to share that list with other sites within the collection.
Solution:
1. Select Edit Page
2. Select Edit within the Webpart and then select Export
3. Save the Webpart
4. Go to the top level of your site
5. Under Galleries select select Web Parts
6. Click Upload and browse to your saved file
7. Give your webpart a name and title
8. Set the Group to Default Web Parts
9. Check Default for Quick Add Groups and Click
Okay Now from any site you can add this new webpart!!!