The prior answers are (I believe) more than adequate for the original question. But for the benefit of others who find this via search, I would like to provide more information.
"Word count" can mean many things. It is not necessarily determined by looking for word boundaries (space and return).
One widely-used measure, at least for U.S. English, is to visualize an old-fashioned typewriter, where each keystroke generates a character (including quote, period, comma, and space). Carriage return is also a character. Then, take the number of characters, and divide by six. This assumes an average word length (in U.S. English) of five letters, plus a space.
The above definition is useful for estimating how many pages will be used in a lengthy, printed book or manuscript. Of course, if you are preparing a PDF with TeX, you know exactly how many pages it uses.
Note that this criterion is not useful for academic papers containing illustrations, tables, and images.
I do not know whether MS Word counts word boundaries, or characters/6. In theory, the result should be almost the same, for lengthy flowing text (U.S. English).
I recently wrote a book, for which the page count measured by characters/6 was 220. The actual page count, using TeX with 5.5"x8.5" layout, was 240 pages including blanks. Not a bad estimate.
You may ask: In the case of a term paper, why not specify number of pages instead of word count? The obvious answer is that the number of pages can be gamed using different fonts, font sizes, or leading.
pdftotext file.pdf - | wc -w, but this also counts page numbers etc. as words.
tex-modehas a word count function: