Classical, country, pop, rock, some satire, a bit of dubstep/tecno stuff, gothic (one eyed doll and voltair mostly) some Japanese stuff, parodies, a little of rap (mostly eminem) new age, metal, crossovers ... A little bit of everything really :)
Movie/video game soundtracks (esp. Legend of Zelda); POWER METAL (HAIL THE BLIND GUARDIAN BARDS!); electronica (Bjork is excellent but might be too weird); indie...I could go on, but it'd take all day.
But I just have a really wide range of tastes.
A TON of Simon and Garfunkel in this apartment. Lots of Loreena McKennitt. I've got a nice alternative playlist made up.
I've found Tycho doesn't like top 40 or electronica (sad), but will happily listen to the podcast "History of Rome" for hours with me contentedly. He tolerates Imagine Dragons for me too... such a sweetheart.
Esmeralda is just constantly wriggling around anyways (unless she's sleeping), so it's hard to tell what she approves and disapproves of. :P