It may be rare for terrestrial planets to be accompanied by satellites, especially large ones. It is far too early for us to draw any conclusions about terrestrial exoplanets (as no terrestrial exoplanet exomoons have yet been detectable), but in our own solar system, only two planets have no satellites, and they are both terrestrial planets: Mercury and Venus. Mars has two small satellites that are almost certainly captured asteroids from the adjacent asteroid belt rather than primordial moons, and that leaves only the Earth among the terrestrial planets to host a large satellite, though it, too, is almost certainly not primordial. Only the giant planets (Jupiter, Saturn, Uranus, and Neptune) have large systems of satellites, at least some of which may have formed while the planet itself was forming.
Though neither Mercury nor Venus has any natural satellites, Venus is known to have at least four transient quasi-satellites, more generally referred to as co-orbitals. They are:
322756 (2001 CK32)
Comes close to both Earth and Mercury in its eccentric orbit (e=0.38).
Wiki JPL Orrery
2002 VE68
Comes close to both Earth and Mercury in its eccentric orbit (e=0.41).
Wiki JPL Orrery
2012 XE133
Comes close to both Earth and Mercury in its eccentric orbit (e=0.43).
Wiki JPL Orrery
2013 ND15
Comes close to both Earth and Mercury in its very eccentric orbit (e=0.61), and is the only known trojan of Venus, currently residing near its L4 Lagrangian point.
Wiki JPL Orrery
2015 WZ12 is a possible fifth Venus co-orbital candidate. Observations during the next favorable observing opportunity in November of this year will hopefully better determine its orbit and nature.
2015 WZ12
Possible Venus co-orbital.
Wiki JPL Orrery
There is concern that there may be many more Venus co-orbitals, as yet undiscovered (and challenging to discover) that pose risks as potentially hazardous asteroids (PHAs) to our planet.
There are no known Mercury co-orbitals. If any do exist, they will be exceedingly difficult to detect since they will always be in the glare of the Sun as seen from Earth.
Asteroids orbiting interior to Mercury’s orbit (a < 0.387 AU) would be called vulcanoids. I say “would be” because none have been discovered yet, though in all fairness, they will be extremely difficult to detect.
A spacecraft orbiting interior to Mercury’s orbit looking outward would be an ideal platform for detecting, inventorying, and characterizing all potentially hazardous asteroids (PHAs) that exist in the inner solar system. A surveillance telescope in a circular orbit 0.30 AU from the Sun would orbit the Sun every 60 days.
The Parker Solar Probe, scheduled to launch later this year, will orbit the Sun between 0.73 AU and an extraordinarily close 0.04 AU, though it will be looking towards the Sun, not away from it. The Near-Earth Object Camera (NEOCam) is a proposed mission to look specifically for PHAs using an infrared telescope from a vantage point at the Sun-Earth L1 Lagrangian point.
References
de la Fuente Marcos, C., & de la Fuente Marcos, R. 2014, MNRAS, 439, 2970
de la Fuente Marcos, C., & de la Fuente Marcos, R. 2017, RNAAS, 1, 3
Sheppard, S., & Trujillo, C. 2009, Icarus, 202, 12