I'm looking to learn 10-15 Brazilian songs, to build a basic repertoire of music which people of Brazilian descent are likely to recognize. Which songs would you recommend I look at/learn?
The ones you can't miss were already mentioned: Aquarela do Brasil (Watercolor of Brazil) and Garota de Ipanema (Girl From Ipanema). The first one is also known as just "Brazil" or "Brazil Theme" worldwide, so it's probably the song people most associate with Brazil.
Having said that, most of the songs people will recognize are from the genres bossa nova, choro and samba. You should look at the "hits" of composers like Tom Jobim (Antonio Carlos Jobim), João Gilberto, Baden Powell, Pixinguinha, Valdir Azevedo and interpreter Elis Regina. Some of my personal favorites include:
Tom Jobim - Wave (Bossa)
The list could go on forever, but do explore the work of these artists and you will end up with dozens of songs in no time.
@RafaelAlmeida, @HubertCzerski and @blueberryfields answers and its comments have already a nice list of musics.
But if you want some musics currently more popular, I recommend you to choose some music from following artists:
- Roberto Carlos (e.g: Detalhes; Eu sei que vou te amar; Como é grande o meu amor por você)
- Ivete Sangalo (e.g: Deixo; Não Precisa Mudar; Agora Eu Já Sei)
Some other popular music you can encounter in this Wikipedia list of "most sold music": http://pt.wikipedia.org/wiki/Anexo:Lista_de_recordistas_de_vendas_de_discos_no_Brasil