Microsoft Word includes a feature called "Auto Correct" which is enabled by default. This feature replaces standard ASCII characters with extended ASCII characters. To see the problem, type (don't copy and paste) the following lines into a blank e-mail message:
don't "quotes"
You should see "straight quotes", the exact characters you typed on your keyboard. Then, type the same lines into a blank Word document. If AutoCorrect is enabled, you will see that Word changes the quote characters as you type, from "straight quotes" to "curly quotes". The problem is that these "curly quotes" are not standard ASCII characters but part of an extended character set. The same thing happens for several other characters, including the hyphen and the apostrophe.
Now, if your recipients' computers all have that same default character set, the message may still look okay to them. And it'll probably look fine if you send a copy to yourself, because you have the required character set also. But when sent to recipients who do not have the same default character set on their computer, those "curly quotes" will be displayed as something else, often making the message very hard to read.
THE SOLUTION
1. Compose your message directly in your e-mail program, or in another application which does not have AutoCorrect.
2. OR... at least disable the AutoCorrect feature. For Word 2003, select Tools -> AutoCorrect Options -> AutoFormat As You Type, and uncheck the first five checkboxes. Click the AutoFormat tab, and again uncheck the first five checkboxes under Replace.
For more in-depth discussion and history behind this issue, click here or here.