After much searching online, I found there was no 'clear' solution to this.
Joyfully, the fix is actually very easy (at least for me, hopefully for you as well!). So far, there seems to be 2 big causes to this issue: you have the wrong COM port selected (the IDE does not see your board) and/or your Arduino drivers are not set properly.
Unlikely Cause: Bootloader is missing
Before we begin, we should check the bootloader of the Arduino for comprehension. If the bootloader is gone or corrupt, this can cause the issue.
To do this: power and reset the board. Check to see if the pin 13 built-in LED lights; if it is not then your bootloader may be missing. If this is the case, then your problem is beyond the scope of this guide. I would suggest visiting this Sparkfun guide: http://www.sparkfun.com/tutorials/247.
If the LED lights, then your bootloader still exists.
Cause #1: Wrong COM Port
With the Arduino plugged to the computer, open "Device Manager" and check the "Ports". Check to see if an Arduino device is listed here; if it is, then make note of which COM port the Arduino is on and check that you have this selected in the Arduino IDE (Tools -> Serial Ports). If the COM port your board is on does not show within the IDE, then try different USB ports.
If you can't even see "Ports"; then for some reason, your computer isn't even recognizing that a device is plugged into it. Test your computer by plugging other USB devices into that port. Possibly your Arduino fails at life; try it with other computers.
Cause #2: Drivers not Installed
If you don't see an Arduino device listed under Ports; then you are probably seeing an "Unknown Device". Check to make sure that "Unknown Device" is indeed, the Arduino by plugging and unplugging the board from the computer. "Unknown Device" should appear and reappear. Assuming this is the case, you will need to install the drivers manually for your Arduino. Windows XP, Vista and 7 users may continue with the guide; if you are a Windows8 user, then please make reference to the comment left by finnigan16 below.
Right click on that "Unknown Device" and select "Properties". Click on the "Driver" Tab (Picture 2; Note: In my Picture 2, I already have the driver set, hence why my window reads "Arduino UNO R3 (COM4) Properties", when yours will probably read "Unknown Device Properties").
Select to "Update Driver..." and then choose to select the folder containing the driver on your computer. Conveniently, you already have the drivers for the Arduino on your computer when you installed the Arduino IDE. Navigate to within the Arduino files (where your .exe is; it'll probably be in your Downloads if you didn't move it. In the third picture, you can see my pathway to the drivers folder) to the "drivers" folder and choose the folder. The computer should automatically choose to install one of the drivers within the folder you selected. Simply proceed with the installation and that should fix the problem.
Make sure the Serial Port is then selected correctly!