Most citation management programs provide ways to convert citations into common formats for transferring into other programs (i.e. from Refworks to Zotero, or Refworks to Mendeley). Below are links to instructions for doing this.
Note: You are not currently able to drag and drop anything other than PDFs into a personal collection in Mendeley Reference Manager.
If you want to keep your folder structure, you will need to export each folder individually and create folders in Mendeley that replicate the folder name in RefWorks. For best results export no more than 500 references at a time.
Zotero makes it very easy to switch managers. The instructions below are for EndNote, but they easily translate to other systems.
At a most basic level the process is: 1) Export citations as a file in some format from your starting application. 2) Import that file into your new application.
There is a detailed guide from Georgetown University Library at: Migrating Bibliographic Data from RefWorks to Zotero
Note: Folders in RefWorks cannot be moved to Zotero along with your references. In Zotero folders are called collections. You will need to create new collections in Zotero that correspond to your folders in RefWorks if you want to preserve your folder structure.
Note: You cannot automatically transfer file attachments (e.g. PDF files) from RefWorks into EndNote. You would have to manually attach the file attachments or use Find Full Text in EndNote or use the File / Import feature in EndNote to import a folder of file attachments downloaded from RefWorks.