How do I override the theme_table() function of the Drupal core in my theme? I just wrote another function named theme_table() in my template.php file, but the default theme_table() is still in effect.
It sounds like your template.php file isn't being read, because having two functions with the same name should trigger an error. Try renaming your theme_table() function to THEMENAME_table() (where THEMENAME is the name of your theme) or to phptemplate_table().
If that still doesn't work, try clearing your theme cache.