Yes, it will work with Mountain Lion. However, its continuing reliability is waning, so I recommend you might upgrade to Office 2011 or you can consider these options:
You can try the freeware suite, Libre Office, that is functionally similar to Office 2007 for Windows except it works on Lion/Mountain Lion. Note that this and following options are not 100% compatible with Office.
You may want to consider as well:
These two suites are similar to Libre Office but not as current or as well-supported:
NeoOffice
Open Office
And, then there is Apple's iWork suite:
Pages - word processing and layout
Keynote - presentation
Numbers - spreadsheet
Each can open and save Office compatible files. They may be purchased separately via the Mac App Store for $19.99 each.
As for other software, any PPC-based software will not run in Lion or Mountain Lion because Rosetta is no longer part of OS X. You will need to upgrade to Intel versions of the software.
(Access to the Mac App Store requires Snow Leopard 10.6.6 or higher and an Apple ID.)