From MozillaZine Knowledge Base

Edit your userChrome.css file to add the code you need, as follows.

/* Display the tabbar at the bottom */

1. content > tabbox { -moz-box-direction: reverse; }

Move it to the Left/Right Sides

/* Display the tabbar on the left */
#content > tabbox {
  -moz-box-orient: horizontal;
}

.tabbrowser-strip {
  -moz-box-orient: vertical;
  /* note: you can set this to -moz-scrollbars-vertical instead,
     but then the scrollbar will *always* be visible.  this way
     there is never a scrollbar, so it behaves like the tab bar
     normally does */
  overflow: -moz-scrollbars-none;
}

.tabbrowser-tabs {
  -moz-box-orient: horizontal;
  min-width: 10ex;   /* you may want to increase this value */
  -moz-box-align: start;
}

.tabbrowser-tabs > hbox {
  -moz-box-orient: vertical;
  -moz-box-align: stretch;
}

.tabbrowser-tabs > hbox > tab {
  -moz-box-align: start;
  -moz-box-orient: horizontal;
}

/* remove the close-tab button */
.tabbrowser-tabs > stack {
  display: none;
}

If you want to move it to the right, add the following lines to the above:

/* Instead, display the tabbar on the right */
#content > tabbox { -moz-box-direction: reverse; }

Unabashedly stolen from clav.

Note that this does not work for Firefox 2.0b2 and newer.