You have to pick:

Assuming Earth and Sun don't change their momentum when they do this, I think Earth would still be in the same orbit around the Sun that it had before. However, all the other objects orbiting the Sun are going to get a very rude surprise. This will be especially catastrophic for the inner planets (Mercury, Venus, Mars, and the asteroids). They're going to suddenly find themselves in a random assortment of elliptical orbits that almost certainly cross each other in new and interesting ways. So Earth could well be destroyed or have its orbit disrupted by a close pass from one of the other planets, and it's certainly going to get pummeled by asteroids on a regular basis from here on. If we luck out and the other terrestrial planets get ejected from Earth-crossing orbits quickly, we _might_ survive as a species. But it'll be absolutely brutal with all those asteroids swarming about.

Earth would almost certainly be destroyed. At the least, our orbit would be changed drastically (if we still had an orbit at all), and we'd all either freeze or burn to death.

Pandemic. I'd like to live, though, and bring about a WORKERS REVOLUTION!

I just went full nerd on this one. I downloaded an orbit simulator from http://www.orbitsimulator.com and actually gave this a go. :)

First, I used the stock solar system that the simulator came with, which happened to be set on January 1 2005. I swapped Earth and Sun's location but didn't change their velocities. When I set time running I saw a couple of interesting things right off the bat. First, thanks to their starting positions Venus and Mercury both happened to be suddenly farther away from the Sun than Earth was. Both of them shot off out of the Solar system. In hindsight, this is an obvious consequence; both of these planets have a higher orbital velocity than Earth so putting them out there with their velocity undiminished meant that they weren't bound to the Sun any more. I don't know if they actually escaped into interstellar space but whether they did or not we won't be seeing them again any time soon. The other interesting thing was that Earth's orbit around the Sun, while just as stable and circular as it had been before, was now retrograde (ie, going in the opposite direction from all the other planets). This has the downside of making any impacts with asteroids a lot more violent. Mars went into a highly elliptical orbit that fortunately didn't cross Earth orbit's, but unfortunately for Mars _did_ cross Jupiter's orbit. In 2035 the two of them will have a close encounter, with Mars passing within the orbits of some of Jupiter's outer moons, but not close enough to disrupt their orbits. I stopped simulating at that point, it looked like Earth was relatively safe.

Then, I ran the stock solar system up to January 1 2012 before pulling the swap again. Once again Mercury gets fired out of the solar system like a cannonball, probably never to return. Venus gets less of a boost this time, however, turning it into a comet-like body with a long elliptical orbit that sends it out beyond Saturn. It's an Earth-crossing orbit so Venus is going to be trouble for us at some point in the future, though its orbital period is over thirty years now so it's unlikely to cause trouble for the forseeable future. Mars, on the other hand, is a more worrying case. It gets dropped into an elliptical Earth-crossing orbit with a period of less than a year. I ran the simulation to 2040 with no obvious signs of trouble, but Earth and Mars kept making close passes so I'm sure there's going to be some sort of cumulative effect on Earth's orbit and therefore on Earth's climate. Should be fine for our lifetimes at least, though, which gives us plenty of time to get cracking on space travel as a backup plan.

So it looks like I was right about the inner planets being potential dangers, and that the exact level of danger would depend on the initial configuration of the solar system at the moment the swap happens. We'll probably be safe for the foreseeable future, though.