When hyphenation is turned on, InDesign typically allows a word to hyphenate between the bottom of one column and the top of the next column, or between the bottom of one page and the top of another. You should try to avoid this "ugly" hyphenation whenever possible. Thankfully InDesign CS3 makes it easy to avoid this. In the Hyphenation Settings dialog box (Control Panel menu > Hyphenation), just deselect the Hyphenate Across Column option. While you are at it, you might want to deselect the Hyphenate Last Word option (introduced in CS2) also. This will prevent hyphenation of the last word of a paragraph, which is also undesirable.
Both of these options are selected by default, so that documents created in previous versions of InDesign don't reflow when opened in CS3. But of course, you can make these settings part of your paragraph styles (you are using paragraph styles, aren't you?) and then you can forget about them.