If we talk about music, each person has its interest. Latvians listen to what the major part of the world listens to, and also in some way to local musicians. If I say we are up to the regular pop music, that would mean it.
But there are also some significant music composers in Latvian history, the first to mention are Raimond Pauls, Imants Kalniņš,
Zigmārs Liepiņš (I've put the link over the last name - you may find some free MP3s there as well to take a listen).
From the rock bands, I would mention
Brainstorm i.e. Prāta Vētra. Greatest mainstream rock band in Latvia so far.
What other interests do Latvian people have? I think they are similar to what everybody has on this planet. They want lots of money, they rate family values, they want a social protection and so on.