Most Windows applications tend to comprise of an EXE file and a number of other peripheral files, such as DLLs, Help files, third party controls, etc that are often placed in different directories on your machine. Mac applications generally come in a package that appear to be a single file to you as a user. In reality there are multiple files to most applications, they are just packaged up to appear as a single file in OS X.
In Windows you generally run a setup program to install an application. It is complete and self contained. On Mac there are a couple of different installation models out there. The most common for downloaded software is to simply drag the application's icon into your Application folder in the Finder. Some install programs will actually place the file in for you, though most require that you drag it in yourself.
A DMG file is a disk image file. Some times you will download an application or series of files that are packaged up as a DMG. Opening it will mount what appears to be a new virtual drive on your desktop. You do not want to run programs from there - drag any applications out of the DMG Finder window and into your Applications folder if you want to run them. You can eject a DMG virtual drive from your desktop (Right Click - Eject) and it will be removed.
The process for uninstalling applications from a Mac are really easy. The vast majority of the time it's merely a matter of dragging the application's icon out of your Application folder and dropping it in the trash. There are some files and settings that applications can leave behind and tools like AppDelete, Hazel and AppZapper help clean that up, though I have not used any of these personally.
Window Sizing is Different
While the Mac OS X windows have what appears to be Close, Minimize and Maximize button in most windows, one of them doesn't work the way it does in Windows. Pushing the Maximize button on OS X will usually make the window as tall as possible for the display area, but not affect the width unless your windows has a horizontal scroll bar.
You can also only size a Mac window by grabbing the lower right corner of the window. The clean, uncluttered UI on the Mac means there isn't a border to grab hold of to resize windows from any edge.
The Alt key on Windows is in the same place as the Command key on a Mac. The Start key on Windows is where the Mac's Alt key sits. Those two keys, more than any other, will cause headaches for you. I've put together this quick guide that should help you at least learn the new common keystrokes.
There Is No Start menu
Most Windows users either toss their application icons on their desktop for easy access or use the Start menu to gain access to their applications. On Mac the Dock bar (by default at the bottom of your screen) is the best place to put the applications you will run most frequently. I highly recommend that you become proficient with the Spotlight feature though. It's an even better way to start applications. This is also the point where people recommend that you go out and get Quicksilver.
There Is Only One Menu Bar
Unlike Windows, which has a menu bar within each application, OS X has only one menu bar that changes options as you switch between applications. If you use a multiple monitor system like I do the get ready to put some serious mileage on your mouse.
Closing An Application Window Doesn't Always Close The Application
In Windows if you close the main window to an application by clicking on the little X button it will shut the application down. On OS X that is not always the case. If the application supports multiple windows (like having multiple documents open at once), then clicking X even on the last open window will leave it open. The best way to quit an application in OS X is to select Quit from the application's main menu. I always just hit Command-Q now.
Killing Off A Non-Responsive Application
In Windows if you need to kill an application that stops responding you can activate the Task Manager, select that application from there and close it. In OS X you click on the Apple menu and select Force Quit, select the application and force it to quit.
The Tab Key Doesn't Work In Every Control
By default OS X does not allow you to tab through every single control. This is a major pain on things like Web Forms that contain check boxes and radio buttons. This is easily address in OS X Leopard by going into System Preferences / Keyboard & Mouse / Keyboard Shortcuts and changing the option on the bottom to make the Tab key work with all controls. Do that right away and save yourself some frustration.
The Missing Backspace Key
What is labeled Backspace on Windows is labeled Delete on Mac - they perform the same action though. The Delete key on Windows is the Delete Forward key on Mac, again performing the same function. If you happen to get a MacBook you will notice that several keys are missing, which is why the keyboard feels so roomy in such a small space. Here is a list of how you can gain access to those missing keys on a MacBook.
So there you have it - the most common problems for me when I first made the switch. There are tons of great features in OS X that you should plan on learning about and I've got numerous posts that cover the ones I've settled in with. The list of applications and features that I've adopted have changed from my first month to my second and into my third month of use.
The advice I would give to recent switchers from Windows to Mac is to try and embrace the way Macs work rather than try to make your Mac work like Windows. Much like moving to a new neighborhood, I can look around and complain that I don't know any of my neighbors and rip on the fact that there is no decent Thai food nearby OR I can make new friends and explore the new cuisine options. Attitude is everything.