1. 20th century classical. I really love Shostakovich, Stravinksy, Bartok, and others who blended "classical" elements (18th and 19th centuries) with modern ideas. At its best, their music is as rich and enjoyable as Mozart and Beethoven, but unusual and fresh at the same time.
2. Contemporary minimalism. (Contemporary maybe meaning 1960s and on.) Especially Arvo Part, Gorecki, and John Adams. Beautiful, haunting, original, and accessible. If you're looking for recommendations, try Fratres and Tabula Rasa by Arvo Part, or Symphony #3 by Gorecki. Really unbelievable music.
3. Bach. 300 years old, and better than anything that's come since. He rides the tension between simplicity and complexity, beauty and the sublime. If humans are still around in 20,000 years, when they look back to the 1000's, they'll think of Bach and Shakespeare. Recommendations: cello suites, cantatas, St. Matthew's Passion, and everything else.
(edit) I'm less experienced with visual art, but Kiki Smith definitely deserves a mention. I also enjoy Gerhard Richter, Kandinsky, Chagall, and Klee.