What software can replace AppleWorks on a new Mac? I just purchased a new Mac Mini, replacing an ancient iMac with AppleWorks. I use that software for email, web-browsing, word processing, spreadsheets and an occasional database. 

Is there a package like Appleworks?  

All I'm seeing is Pages, Numbers, etc.  What can replace these functions?
There isn't a perfect fit for a unified Appleworks replacement - but each of the 5 functions is available directly from Apple either pre-installed or on the App Store.
Apple now has the iWork suite, which used to be a single package you can buy, but is now separate apps on the App Store. It is made up of Pages (word processor), Keynote (presentation software), and Numbers (spreadsheet). If you want a database consider Bento or FileMaker Pro. All five are made by Apple (the databases are made by FileMaker, an Apple subsidiary). Bento equates to Access, and FileMaker equates to MS-SQL (roughly).  Of course the mail app is the fifth item you will use to fully replace Appleworks.
Edit: Bento is no longer an option.  FileMaker ceased production/support of Bento.  There are other options like TapForms at http://www.tapforms.com.