With its usual spots, you can clearly see the sun's rotation. But as a pristine, spotless orb, it's a little harder to see its movement.
Humans foolish enough to gaze directly at the sun will likely perceive a uniformly-colored orb. But this miasma of incandescent plasma isn't actually all that pristine: the star's surface is usually peppered with dark spots created by magnetic activity.
Lines of the sun's magnetic field pop out of its surface in bundles called pores, and when pores get too close to one another they squeeze the plasma between them to form relatively cool spots—3,800 degrees Kelvin in contrast to the rest of the surface's 5,800 K or so temperature. Intense bursts of radiation called solar flares pop out of these plasma squeezes, and that radiation can wreak havoc on various electrical systems on Earth.
Sunspots have been monitored daily since 1849, and all that data has shown that their frequency waxes and wanes in an 11-year cycle. Other kinds of solar activity can still impact Earth while sunspots are sparse, but they serve as a decent index for the overall intensity of space weather.
As you can see from the image below, which was taken by NASA's Solar Dynamics Observatory (SDO), our sun is looking pretty smooth these days. According to NASA, SDO returned spotless images of the star for 15 days straight starting on March 7, which marks the longest stretch of spotlessness since 2010.
NASA's GSFC/SDO/Joy Ng
The image on the left shows sunspot activity from the sun's last "solar maximum"—an extreme period at one end of the solar cycle spectrum. The peak activity of the sun's last cycle occurred in the spring of 2014. We're not at the solar minimum yet, in all likelihood—based on the 11-year cycle schedule, we can expect that to happen sometime during 2019 or 2020. But NASA scientists say that the recent fortnight of sunny-side-up sun indicates that solar activity is winding down towards this low period just as we'd expect.
And the sun acting normal is a very good thing. Between 1645 and 1715 the sun eschewed its usual patterns of activity, casting the 11-year cycle aside in favor of a long stretch of minimal sunspots. This corresponded with a "little ice age" categorized by bitter winters. And you thought the polar vortex was a pain.