Aside from the history and art museums of Rio (that I have put in their own sections) there are quite a few others. I picked some of them out:

Museu Nacional
Description: The National Museum of Rio de Janeiro is typical as such, it has no real focus but a little bit of everything. Sections with archeology, zoology, Egyptian mummies and weapons used by the indians etc. One of the more impressive pieces is a 5 tonne meteorite.
Address: Parque 5a da Boa Vista, São Cristóvão map
Open: Tue-Sun 10h/16h
Phone: 2568-1149
Site: Museu Nacional

Museu das Telecomunicações
Description: One of the newest additions to the museums of Rio. The exhibitions are about the history of communications in all it´s guises. They also have many events. Free entrance.
Address: Rua Dois de Dezembro 63 6th floor, Flamengo map
Open: Tue-Sun 11h/17h
Phone: 3131-3060
Site: Museu das Telecomunicações

Real Gabinete Português de Leitura

Interior of Real Gabinete Português de Leitura, photo by Andreas Lönngren.

Museu do Universo – Planetário
Description: A museum about the universe. With various models and experiments tries to explain different phenomena like low tide and solar eclipses. Also has an historical angle where the development of astronomy and astro physics are explained in short. An interesting part is where space travel and the life on other planets are discussed. Does not have a telescope. One of the more modern museums of Rio de Janeiro.
Address: R. Vice-Governador Rubens Berardo 100, Gávea map
Open: Tue-Fri 14h/18:30h Sat, Sun and holidays 15h/19h
Phone: 2274-0046
Site: Museu do Universo

Biblioteca Nacional
Description: The National Library is not really a museum but I think it deserves a place on this list. With over 8 million titles it is the most complete collection of books in South America. It has volumes and documents of worldy interest and is a must if you are in to bibliography.
Address: Av. Rio Branco 219, Centro map
Open: Guided tours weekdays at 11h and 15h, book them on 2220-9484
Phone: 2262-8255
Site: Biblioteca Nacional

Real Gabinete Português de Leitura
Description: This absolutely stunning library built in the end of the 19th century is well worth a visit, many very rare books are kept here. More than a library open for resaerch they also have exhibitions.
Address: R. Luís de Camões 30, Centro map
Open: Mon-Fri 9h/18h
Phone: 2221-2960
Site: Real Gabinete Português de Leitura

H Stern Museum
Description: This museums is in place to sell jewelry. But it doesn´t stop it from being quite interesting. On display are numerous precious stones as well as explanatory models of mining. You also get to see the workshops (through super thick glass). It’s free.
Address: R. Garcia de Ávila 113, Ipanema map
Open: Mon-Fri 9h/18h Sat 9h/12h.
Phone: 2106-0000
Site: Museu H Stern

DNPM – Museu Ciências da Terra (Museum of Earth Science)
Description: This museum has a geological focus displaying lots of stones and a fossile collection. It also has some fragments of meteorites. Free entrance.
Address: Av. Pasteur 404, Urca map
Open Mon-Fri 10h/16h
Phone: 2295-0032;438
Site: No site

Museu de Astronomia e Ciências Afins
Description This Science museum displays methods and instruments used in the past. The most interesting part is that days when the museum is open at night (Wed, Sat and Sun) vistitors can have a look at the stars in the telescope from the 1830´s.
Address: R. General Bruce 586, São Cristóvão map
Open: Tue, Thu, Fri 10h/17h Wed 10h/20h Sat, Sun 16h/20h
Phone: 2580-7010
Site: MAST

If you have suggestions on other good museums of Rio just contact me and I will put them in.