Scott did a great job on this but he is incorrect at several points. Just so no one is left confused:
1) There is physical evidence for negative mass. It has been created in the lab and its effects observed, so the "negative energy theorem" of old really has been overthrown, and those who study this subject do think wormholes are possible.
Washington State University physicists have created a fluid with negative mass, which is exactly what it sounds like. Push it, and unlike every physical object in the world we know, it doesn't accelerate in the direction it was pushed. It accelerates backwards.
2) Wormholes do not connect different universes. Wormhole theory does not require there be more than one universe. Wormholes connect two different spacetimes within the universe. Kip Thorn actually created wormhole theory in response to his friend Carl Sagan who was looking for arbitrarily rapid spacetime transport. He asked Kip if he could use black holes for this. Thorn went away with his grad students at Cal Tech to figure this out, and found that no, you cannot use black holes, but you can use wormholes. Sagan wrote Contact as a result, and the Stargate movie and TV series all followed. The science preceded the fiction. Dr. John Cramer of Transactional Quantum Mechanics fame actually has a theory for how to steer wormholes. Unlike the TV series, you do not need gates at both ends to open a wormhole.
3) Scott draws a distinction between gravitational and spacial lensing, but this is incorrect. According to Einstein's General Theory of Relativity (upon which all modern gravity physics rests--including wormhole theory) mass tells space how to curve and space tells mass how to move. The distinction between gravitational and spacial lensing is a distinction without a difference, and all physicists call it gravitational lensing. Because of this, all wormholes have gravitational effects and will indeed tear matter apart unless they are of sufficient size that they can be considered "absurdly benign wormholes" and these require about a Jupiter mass of exotic matter with negative mass and negative inertia to hold the throat open. That's not as hard to do as one might guess. If you're curious, read Woodward's book below. Point is though, if you understand GR, you understand that technically, there is no force of gravity, or if you choose to say there is, it does not act upon mass but rather upon spacetime itself. Mass bends space and space tells that mass how to move. Still, physicists speak of gravity all the time, and unless a wormhole is benign, it will disassemble matter.