Have you heard of Maná? They are a Mexican band and they have some very nice songs.
Also Vicentico, who's an Argentine singer and member of the former band Los Fabulosos Cadillacs, has recorded very good songs. Another Argentine singer who has some nice songs is Diego Torres.
Then you have some other pretty famous bands like The Mexican band Café Tacuba, which I really don't know much about, or Argentine band Soda Stereo, which is a rock band. Many people in Latin America love Soda Stereo, I can't say I'm one of them, though.
There's also an Uruguayan singer called Alejandro Drexler, I've listened to some of his songs and I liked them all. He's good. He won an Academy award for writing the song "Al Otro Lado del Río" from The Motorcycle Diaries
Of course there are many, many more bands and singers, but these are the ones that I could think off the top of my head.