There are quite a few Rio history museums. It is Brazil´s dynamic history and as well the particular events in Rio de Janeiro that are the general themes. I have picked out a few here:

MHN (Museu Histórico Nacional)
Description: This is the most important historical museum in Brasil. Big exhibitions from enormous archives in two big old buildings. If you look up the word museum in dictionary, this is what you would see.
Address: Praça Marechal Âncora, Centro map
Open: Tue-Fri 10h/17:30h Sat, Sun 14h/18h
Phone: 2550-9224
Site: MHN

Museu da República
Description: During the period between 1897 and 1960 this was the White House of Brazil. Well organized and with lots to offer for the visitor with an interest in Brazilian politic history. Entrance free on Wednesdays.
Address: Palácio do Catete, R. do Catete 153, Catete map
Open: Tue-Fri 12h/17h Sat, Sun 14h/18h.
Phone: 3235-2650
Site: Museu da República

Folclore Edison Carneiro
Description: Not very known but still a really interesting museum showing the history of the people of Brazil. Cultures, customs, clothing, rituals and art. Gives you a little clue to why and how the modern Brazilian culture came to be.
Address: R. do Catete 181, Catete map
Open Tue-Fri 11h/18h Sat, Sun 15h/18h
Phone: 2285-0441
Site: No site

Museu do Índio
Description: One of the Rio history museums I personally recommend. With it focus on describing the various indigenious cultures of Brazil it is very interesting and can give you important insights in how this country has derived lots of its culture from the Indians and how the customs lives on in various instances of modern Brazilian society. Well worth a visit if you have an interest in culture.
Address: R. das Palmeiras 55, Botafogo map
Open: Tue-Fri 10h/17:30h Sat, Sun and holidays 13h/17h
Phone: 2286-8899
Museu do Índio