At work I am currently working on AutoCAD 2000. I want to know... If I copy these dwg files in AutoCAD 2000 (at work) will I be able to open these files in AutoCAD 2009 (at home)?

Yes, AutoCAD is upwards compatible - e.g. AutoCAD 2010 can still open and read DWG files from AutoCAD V2.6.

All the software that are used are always compatible for higher version but some has facilty of coming back to previous version. Generally only 3D software like solidworks, inventor, Pro-E etc. are not compatible to lower version.
In general you can easily migrate from lower to higher but not vice versa.
 
Tom
www.indovance.com