There are three keyboard shortcuts in InDesign (and InCopy) that insert a "break" character in your text. This character forces all the text after the character to jump to the next column, frame or page. The shortcuts are:
|Column break|| |
|Frame break|| |
|Page break|| |
(Note that these shortcuts all use the enter key on the numeric keypad. You cannot substitute the return key. If you do not have a full-size keyboard with a numeric keypad, you can substitute fn + return on most keyboards for the enter key.)
This "break" character is displayed on the screen as an odd little upside-down carat character when Type > Show Hidden Characters is chosen. So, to remove the column, frame or page break, just delete the break character.
Contrary to Adobe's documentation, these shortcuts work with long, multi-page tables as well as text. Just click with the Type tool on the row that you want to move to the next page and press the shortcut for either Column break or Frame break. This will force this row of the table to jump to the next column or frame (or page, if that is where the next column or frame is located).
If you later wish to delete the break, you will find that there is no visible "break" character in the row where you entered the keyboard shortcut. When you use the keyboard shortcut for column break or frame break in a table row, InDesign actually changes the Table > Cell Options > Rows and Columns "Start Row" setting to In Next Text Column or In Next Frame. So, to remove a break that you've inserted in a table, put your text cursor in the first row after the break, choose Table > Cell Options > Rows and Columns and change the "Start Row" to Anywhere.
(Tested in both InDesign CS2 and CS3). See also this related blog entry.