If you mean a singular object instead of clusters of stars (galaxies) or clusters of galaxies (superclusters), then I will provide my list (that we know of so far):
Largest non-spherical solid object: Haumea - 620 km radius.
Largest moon: Ganymede - 2634 km radius.
Largest rocky planet: Kepler 10 c - 2.35 Earth radii (15,000 km).
Largest gas giant planet: HD 100546 b - 6 Jupiter radii (419,466 km).
Largest ring system: J 1407 b - 0.6 AU radius (90 million km).
Largest star: UY Scuti- 1708 Solar radii (1.19 billion km).
Largest black hole: TON 618 - 1300 AU radius (194.5 billion km).
Largest (mostly intact) nebula: LAB-1–300,000 light year diameter.
As mentioned before, as a bonus:
Largest galaxy: IC 1101- 3.92 million light year diameter.
Largest structure: Hercules-Corona Borealis Great Wall - 10 billion light year diameter.
UPDATE 2020:
Stephenson 2-18 is now considered to be among the largest known stars, if not the largest, with a radius of 2,158 solar radii. UY Scuti on the other hand is about 1,700 times greater than the radius of the sun. It is also among the most luminous cool supergiant stars, with a luminosity of 440,000 solar luminosity.
Update 2023:
The largest black hole discovered so far is Phoenix A from the Phoenix Cluster. It is around 100 billion times the mas of the Sun and has an astounding radius of around 1950 Astronomical Units (295.25 billion kilometers).
