Did you do any permanent damage? No, probably not.
In general, you want to shutdown a computer, using the proper protocols for that system. For Windows, go to Start and shutdown the system. Otherwise you do risk damage. Even a toaster, a basic mechanical device that heats bread, can be damaged if you were to yank out the power cord while the heating coils were turned on.
The issue at hand is the complexity of the machine, and in this case, the complexity of the software running on it. Windows, for example, runs a huge paging file, which is sort of like "virtual memory". This file is constantly being read to/from by Windows, and if you turn off the computer while it's busy writing to this file, it could be damaged. And a damaged paging file will basically screw up the computer irreparably, requiring a reinstall of Windows. That may be a repair install, but could potentially be a full wipe and virgin install -- and the latter option isn't much fun, as it means reinstalling all of your software, losing all your system preferences in Windows and various programs, and restoring all your work/data files. All of this because you turned off the power the wrong way.
Hardware can be damaged, too, such as a hard drive crashing a platter during write, or a CD or DVD burner/ROM laser being damaged while it was reading/writing a disc.
It's just not pretty, when something goes wrong, so be careful!
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