This has happened to me many times in Microsoft Word when trying to export a simple manuscript to PDF. A 5–8 page Word document, ~50 KB in size, will end up as a 10+ MB PDF file, which is far too large to reasonably email to someone.
Rene's answer is on the right track—the problem is that fonts get embedded into the document—but just using one of the standard typefaces won't necessarily solve the problem.
All of my documents were in Times New Roman, using nothing fancier than bold and italics. Or so I thought. It turns out that I have automatic kerning enabled in my default template (for obvious reasons). When exporting to PDF, Word was actually embedding each of those ligatures as a separate font object into the document, bloating it beyond all belief.
The fix is simple, you just have to remember to do it each time:
- Select all of the text in the document.
- Format → Font → Advanced
- Uncheck "Kerning for fonts"

Interestingly, you can leave ligatures, contextual alternatives, and other advanced typography features enabled; they have no perceptible effect on the size of the resulting PDF.
Re-export the document as a PDF, and it's down to a hundred or so KB. Unfortunately, the kerning is sub-par, so I wouldn't recommend printing this way, but it works fine for emailing a document.