Can I run a .exe file on a Mac?

Hi

I need to know know if it's possible to run a '.exe'
file on an Intel-based Mac running Mac OS X.

Short answer: no.

There's a CD with an application I need to run. In the Finder
it has the icon of the black computer screen with
green letters and it's titled 'startCD.exe. It'll run
on Windows but due to circumstances I need to run it
on my computer. Any direction you can point me
in will be greatly appreciated.

You can install BootCamp or Parallells as a Windows environment (you will need to install a Windows Operating System thereafter – XP Pro etc) that will then allow you to run .exe files

Maybe:

http://www.codeweavers.com/
"CrossOver Mac allows you to install many popular Windows applications and games on your Intel OS X Mac. CrossOver includes an easy to use, single click interface, which makes installing Windows software simple and fast. Once installed, your application integrates seamlessly in OS X. Just click and run your application directly from the OS X Finder. Clicking a Windows file or document — including email attachments — will launch the appropriate Windows program, allowing you to work on the files. Best of all, you do it all easily and affordably, without needing a Microsoft operating system license.

Adding new Windows software is easy. Just place your install CD in your Intel Mac, and CrossOver will recognize it and offer to begin the installation process. CrossOver then completes the installation and configures your application to run on your Mac. That's all there is to it."

No need to waste your money. Try it free, if it doesn't work then don't buy it. Not all .exe's are supported or guaranteed to work, but some might. Seems to be still in development.

http://www.codeweavers.com/products/download_trial/