OS X Mountain Lion isn't compatible with PowerPC applications, being that the reason why those applications don't work.
I always recommend to check that your applications are compatible and to update them before upgrading Mac OS X, so you don't have those problems.
Now, if you want to run those applications, one thing you should consider is the possibility to buy Mac OS X Snow Leopard Server and install it onto a virtual machine (using Parallels, VMware Fusion or VirtualBox). It's not difficult to install it, but I don't recommend this option. You will be wasting time and money, and you will get less performance when you run the virtual machine, apart from the fact that you will be using outdated applications.
The best option is to upgrade those applications. Office 2008 and 2011 are compatible with OS X Mountain Lion, and respecting to Quicken, it was released a Quicken 2007 version compatible with Lion and Mountain Lion > http://quicken.intuit.com/personal-finance-software/quicken-2007-osx-lion.jsp
If you don't want to pay for Office, you can go to another productivity suite like LibreOffice, free and open-source, and all your documents will work with it