It sounds like you're running afoul of Word's smart-selection features. Choose Tools » Options, click the Edit tab (see Figure 3-3), and see whether the "When selecting, automatically select entire word" and "Use smart paragraph selection" boxes are checked. If so, try unchecking them, and see if you prefer the resulting selection behavior.
Figure 3-3. Many of the options on the Edit tab of the Options dialog box annoy nearly as many people as they help.
If you check the first box ("When selecting, automatically..."), when you drag from the beginning of a selection to another word, the selection is automatically extended to encompass both wordseven if you deliberately dragged from the middle of the first word. As you extend the selection from two words to three, Word selects a word at a time, rather than partial words.
If you check the "Use smart paragraph selection" box and carefully try to select an entire paragraph minus the paragraph mark, Word will grab the paragraph mark anyway. As usual, Word is trying to be helpful, but many people find this kind of help annoying. (If you want to see your paragraph marks, click the Show/Hide button on the Standard toolbar or choose Tools » Options, click the View tab, and check the "Paragraph marks" box.)
Word 2000 offers neither smart paragraph selection nor most of the smart-cut-and-paste settings.