By and large, Adobe (and Macromedia before them) have gone to great lengths to ensure backward compatibility where appropriate; so the rule of thumb is that you should be fine.
First and foremost, I would make use of ColdFusion's Code Compatibility Analyzer. It is available as part of the free Developer Edition, if you want to check before upgrading.
You can find it in the ColdFusion Administrator, in the Debugging & Logging section, as "Code Analyzer".
As it says on that page:
The Code Compatibility Analyzer helps migrate your applications to ColdFusion from earlier versions of ColdFusion.
The Code Compatibility Analyzer reviews the CFML pages that you specify and informs you of any potential compatibility issues. It detects unsupported and deprecated CFML features, and outlines the required implementation changes that ensure a smooth migration.
If the Analyzer doesn't find any issues, I would then encourage you to install the developer edition and run your unit tests. (You have unit tests, right?)
If you don't have unit tests, your only other option is just to test everything manually. Good luck!
One final approach is to read the release notes for versions 8 and 9, as well as the 8.1 and 9.1 point-releases. Adobe and Macromedia were meticulous about documenting precisely what changed, which should prove helpful for you. The release notes are available as PDF for both versions 8 and 9 from Adobe.