Curiously, even Galadriel doesn't rule over the elves of the golden wood alone--she rules them in conjunction with Celeborn (who is pretty much a non-entity in the theatrical release of the LotR movie although he has a slightly more significant role in the extended edition DVD). Galadriel is just the more personally powerful of the two and the one who bears the ring of adamant (although interestingly, in the book Celeborn was considered the wiser).
In Tolkein's works, there weren't any elven queens who exercised sole rulership over their people.
Feanor and his seven sons, Finwe, Fingolfin, Fingon, Turgon, Finrod Felaugund, Thingol, Gil Galad, and Thranduil were the kings of the elves whose names I can remember off-hand. Galadriel was mentioned among them as one of the leaders of the Noldor at the time of their exile from the blessed lands though she was not a queen. (And did not become High Queen of the Noldor after the death of Gil Galad). Melian, queen of the hidden kingdom of Doriath was usually mentioned along with Thingol but she was not an elf and after Thingol's death, she withdrew and Dior the fair.
Elven women don't appear to have been counted in the succession either--at least not apart from their husbands. Thingol's grandson ruled the kingdom. And after Finrod's death, Nagrothrond doesn't appear to have a named ruler until Turin Turambar became its war leader and his pride led to the city's destruction. After the death of Turgon, Tuor and Idril led the refugees of Gondolin together. (Though neither was given any title). Galadriel did not become high queen of the elves after the death of her brothers or her nephew, Gil Galad (of course, Elrond (the other possible candidate on the basis of succession) didn't either--the role appears to have passed away with the end of the second age).