Today Mercury transits the sun for the last time until 2016! As a reminder -- DO NOT LOOK AT THE SUN WITHOUT APPROPRIATE SAFETY!
For a while, transits lost a lot of their scientific lustre. Since we knew the distances to the planets, the traversal of Mercury across the sun became an interesting phenomenon, but nothing more.
That has changed with the discovery of planets in other solar systems. In some of these systems, the planet goes in front of the star as seen from the earth. We see the star get slightly dimmer (the planet only blocks some of the light, not all of it) and then re-brighten. We can learn a lot about the planet -- its mass, its size, and even its atmosphere, as it passes in front of its parent star.
There are uncertainties, though. What happens to what we observe if the planet passes over a starspot? Or over a flare on the star's surface? Although we can calculate what should happen, it is better to know for certain. And that is where the transits of Mercury and Venus come in to play. With luck, the transits will pass over some of the sun's active regions, and we can observe what, if any, changes there are in what we observe from Earth. We can then apply this knowledge to what we see in transits in other solar systems, and try and figure out if a star spot or stellar flare is messing up our observations.
If it is cloudy where you are, or you don't have a safe telescope, you can watch the transit live online.