You can copy Sitecore users from one instance to another using a package however their passwords will be reset. If you want to copy users without losing passwords The Inside Corner site has a page that describes how to migrate Sitecore users from one installation to another:

This description is a bit out of date if you are using the database script method with SQL Server 2008 R2 because the SSMS wizard has been changed.
Here’s how to do it with SQL 2008 R2:

  1. Right click on the core database and choose Generate Scripts
  2. If SSMS shows an Introduction page, click next
  3. Select specific database objects
  4. Expand Tables
  5. Select all tables with a name starting with aspnet_
  6. Click next
  7. Select the advanced button
  8. Change “Script DROP and CREATE” to Script DROP and CREATE
  9. Change “Types of data to script” to Schema and data
  10. Choose whatever option to save the script that works for you, clipboard, file or new query editor window.

PS: I suspect this would work with any ASP.NET site that uses the membership provider but who does regular sites anymore?