I don’t know why and in a complete and proper move this should not happen, but something has tripped the installer scripts and its trying to create tables that already exist. I’d start by dropping the database and recreating it so you have a completely clean database and then re-import your database dump from your previous site.
Several methods are listed around here for moving from site to site, some of them highly complex and completely prone to frustration and failure, especially the ones that try to save you time or data transfer and especially, the ones that export and reimport product, categories and customers. If you did it right in the original environment, just move the whole thing as it exists.
The procedure for a linux to linux move is distressingly simple. I used to use the following (till I set up rsync) to pull the live site to my local dev server VM. If it was fully functional on the old server, with changes for database credentials, baseURLs and proper file permissions set, it should run on the new server, excepting for any domain specific stuff you may have done in .htaccess
1. Tar Magento installation, move to new system, untar
2. Set file permissions on Magento installation in new system, do this before you proceed to doing anything else!!!
3. Dump database on old system, restore on new system and change baseURLs before you try to access the site in either the front end or back end.
4. Change database access credentials in app/etc/local.xml
5. Find out the other half dozen annoyances on running Magento in its new environment and fix them.
The above simplistic steps are given a bit more detail over here http://www.magentocommerce.com/boards/viewthread/228830/#t322770