Rio [1] has a considerable number of bike paths. Those in search of a languorous outing can take to the paths that line the beaches (stretching from Flamengo [2] to Leblon [3] and then along Barra) and ring the Lagoa Rodrigo de Freitas [4].
Meanwhile, hard-core jocks can take on the steep trails leading into the Floresta da Tijuca [5].
You can rent bikes in many places along the Zona Sul beaches and around the Lagoa. A particularly wide range of models are available at Special Bike (www.specialbike.com.br [6]) in both Botafogo [2] (Rua São João Batista 21-A, tel. 21/2539-0693) and Ipanema [3] (Rua Visconde de Pirajá 135-B, tel. 21/2267-7778) for around R$60 a day.
Links:
[1] http://www.moon.com/destinations/brazil/rio-de-janeiro/rio-de-janeiro-city
[2] http://www.moon.com/destinations/brazil/rio-de-janeiro/rio-de-janeiro-city/sights/flamengo-and-botafogo
[3] http://www.moon.com/destinations/brazil/rio-de-janeiro/rio-de-janeiro-city/sights/ipanema-and-leblon
[4] http://www.moon.com/destinations/brazil/rio-de-janeiro/rio-de-janeiro-city/sights/lagoa
[5] http://www.moon.com/destinations/brazil/rio-de-janeiro/rio-de-janeiro-city/recreation/floresta-da-tijuca
[6] http://www.specialbike.com.br