Planetary system orientation & the search for exoplanets
The multi-planet system HR 8799 is pretty close to face-on. Here's a video made by interpolating images taken over 7 years showing the orbital motion.
The planets of HR 8799 were detected by imaging. The majority of exoplanets have (at the time of writing) been detected by the radial velocity method, which requires radial motion and thus is most sensitive to planets close to edge-on, and the transit method which requires that the planet passes in front of the star as seen from Earth (thus will only spot planets extremely close to edge-on). The imaging method does not have this issue, so can find both face-on planets (like HR 8799) and edge-on ones, like Beta Pictoris b (video).
Astrometry is another exoplanet detection method that would allow detection of face-on systems. It has been plagued by a number of false starts (e.g. the infamous &quot;detection&quot; of planets around Barnard's Star by Peter van de Kamp) but hopefully once the full Gaia dataset is released there will be numerous astrometric exoplanet detections, which may include near-face-on systems.