Was Catherine the Great's reputation deserved?
As a ruler, substantially — she was among the most consequential monarchs of the eighteenth century. As the subject of the story most people know about her, no: the horse legend is a fabrication, and its persistence is itself the more interesting subject.
Dealing with the myth first. The story that she died attempting intercourse with a horse is entirely false. She died in 1796 of a stroke, in her own rooms, aged 67, with the circumstances documented by physicians and attendants. The story appears to have originated in France after her death, among opponents, and spread because sexual slander was the standard instrument for attacking powerful women — the same pattern applied to Marie Antoinette and others.
Why the slander stuck. She was a woman who had taken power by deposing her husband, ruled without one, had acknowledged lovers, and exercised authority in a manner reserved for men. The legend is a political attack that outlived its politics, and it has effectively replaced her record in popular memory.
What she actually did:
Seized the throne in 1762 in a coup against her husband Peter III, who died shortly afterwards in circumstances never satisfactorily explained. She was German-born and had no Romanov blood.
Expanded Russia enormously, through wars with the Ottoman Empire securing access to the Black Sea, and through the partitions of Poland — which extinguished a state.
Corresponded with Voltaire and Diderot and presented herself as an enlightened monarch, founding schools, hospitals, a school for girls of the nobility, and the collection that became the Hermitage.
Codified and reformed administration, and convened a commission to draft new laws, which did not produce a code.
The contradiction that defines her reign: enlightenment correspondence alongside the expansion of serfdom, which she extended into newly acquired territories and declined to reform. After the Pugachev rebellion of 1773–75 she turned decisively conservative.
The judgement historians generally reach: a highly capable, pragmatic autocrat whose enlightenment was genuine in interest and limited in application.