Whenever Star Trek dealt with an alternate universe usually the culprit was 'The Mirror Universe'. It was introduced in 'Mirror, Mirror' of the Original series, where the Enterprise was an Imperial warship of conquest and the crew was very....cuththroat in day-to-day operations. One had to watch his back since rank ascension was faster through assasination.
DS9 capitalized on this idea in some episodes I haven't seen, and Enterprise did a few set in the mirror universe. Presumably the ship in Elite Force was a cruiser that somehow came through the mirror universe and ended up in the Beta quadrant. Given how random Star Trek is on things, this doesn't come as a surprise. Still, we never found out what ship it was...
And now that a 'new' alternate universe has opened up, what are the possibilities of crossing between the mirror and old universes?