Seven Ways to Open EXE Files in Mac OS X
File Juicer

File Juicer does not run EXE files. It searches inside the EXE file to see if it contains images, Flash games or animations, compressed .ZIP or .RAR archives and many other formats. If if finds any, it will extract and save them.
13 second movie showing how to extract images from an EXE file (a screen saver). This will work on some EXE files, but not if the EXE file is encrypted or use a proprietary storage system.
ZIP and RAR files are common inside EXE files which are made "self extracting" on Windows by wrapping them in an EXE file. You open ZIP files by double-clicking them. RAR files require RAR Expander.
Pocket PC applications are often packaged as "Windows only installers" in EXE files, and the developers forget to make an
installer for Mac OS X.
File Juicer can extract the CAB files from the exe file,
and you can manually copy this file to the Pocket PC and get it installed this way.
Adobe/Macromedia's Flash files are also often wrapped inside an EXE file. File Juicer can extract them, and you can play them with iSwiff .
Some EXE files containing other files are not possible to open with File Juicer. Typically this is packages made by installer applications like InstallerVise from MindVision.
Parallels Desktop

Parallels Desktop require a Mac with an Intel processor. It is more convenient to use than Apple's Boot Camp as it does not require to restart your Mac every time you want to run a Windows application.
You still need a copy of Microsoft Windows
and install it on a part of your hard
disk. You also need to keep this part of your disk free of spyware, viruses. You can keep the Mac part of your disk separate
from your Windows part, so nasty applications will not ruin your Mac data.
VMWare's Fusion

If you have a Mac with an Intel processor, VMWare Fusion will be an alternative to Parallels Desktop. They are already known for making virtual Windows environments on Windows, so Windows users can run different versions of Windows on the same PC.
Amazon: VMware Fusion 5 for MAC OS X
You do need a copy of Microsoft Windows
ClamXav - Antivirus

EXE files can be nasty to Windows users. If you want to use any of the applications below to run the EXE file you have, I recommend checking it for virus first. This is a good idea even though Windows viruses will only be dangerous for the part of your hard disk you set aside for Windows: one can never be too careful when running EXE files. Because File Juicer does not run EXE files, but search them for images, Flash animations and more, even infected EXE files are not dangerous when dropped on File Juicer for a search for extractable files.
ClamAV knows about 90.000 viruses. It is free and you can download ClamXav for Mac OS X here.
ClamXav is quite nice as it does not run in the background and slow your Mac down unless you directly ask for it (by launching ClamXav Sentry from the File menu).
Microsoft Virtual PC - requires a PowerPC processor

If you have a Mac with a PowerPC CPU, Microsoft's now discontinued (search on eBay) Microsoft Virtual PC for Mac 7.0 with Windows XP Home which is the most compatible and easiest way to get PC software running on your Mac.
If you already have a Windows CD and a few hours to install it, you can save $35 by buying:
Virtual PC for Mac 7.0 without Windows.
Virtual PC run Windows as a PC about 3 years older than your Mac. To improve performance you can turn off the most CPU hungry features in Windows.
Microsoft's Virtual PC is no longer updated and will never become compatible with Apple's new Macs with Intel CPUs. If you plan to upgrade your Mac soon, Microsoft Virtual PC may not be worth the purchase.
Apple's Boot Camp

You still need to purchase a copy of Windows, install it and keep that corner of your hard disk free of virus, worms and spyware.
Amazon: Microsoft Windows
Crossover Mac

The big advantage of their approach is that you do not need to buy and install Windows.
The disadvantage is that it is not a 100% Windows replacement, but they have focused on the most common parts of Windows, and if an application only depend on those it should work. Their list of supported applications (and database!) give an impression of how much of Windows they support.
Amazon:
Code Weavers Crossover Mac (Mac)
How to avoid EXE files (Where to look for Mac Software)
The 3 most popular places to look for Mac software are: Visit them both as they are different in how they present their lists. MacUpdate and VersionTracker has user reviews of the software too.While all active software developers list their software on these 3 sites, there are more which write about using Mac software. MacWorld.
Alternative Emulators
Alternative emulators are coming and they are a cheaper alternative to Microsoft's Virtual PC. They still require you to install Windows and to spend the time doing so. Virtual Box is likely the most well known.
Emulators run Windows as a PC about 2-3 years older than your Mac. To improve performance, you can turn off the most CPU hungry features in Windows.