Of course there's a lot more to look for in Jupiter's atmosphere than the GRS. That's a good thing, because for something so famous, it can be surprisingly difficult to see. It appears slightly more distinct when Jupiter is viewed through a light green or blue filter.
Below is a calculator you can use to predict the local and Universal Times and dates when the center of the Great Red Spot should cross Jupiter's central meridian, the imaginary line down the center of the planet's disk from pole to pole. Press "Initialize to today" to view the dates and times of the next three transits of the GRS. Or you can enter any date in 2012 or 2013 to find other transit times. The listed times should be accurate to within a few minutes.
The predictions assume the Red Spot is at Jovian System II longitude 173°, based on historical trends noted by JUPOS. If the GRS moves elsewhere, it will transit 1 2/3 minutes late for every 1° of longitude greater than 150° or 1 2/3 minutes early for every 1° less than 150°.
Features on Jupiter appear closer to the central meridian than to the limb and thus are well placed for viewing for 50 minutes before and after their transit times.
Click here for a printable list of all predicted Great Red Spot transits through Dec 2012.