Olafur Arnalds - 0040 Olafur is an Icelandic genius, his music is pretty eclectic -from strings to electronic elements- he is pretty experimental with his sound and his sound has changed over the years. But my favourite of his is still his debut Eulogy For Evolution.
Max Richter - Infra 5 He is probably my favourite contemporary composer, and his minimalist style is pretty soothing. Check out Infra and The Blue Notebooks. He also did a re-composition of Vivaldi's Four Seasons, and the results are pretty amazing; he retains Vivaldi's feel while adding some of his own contemporary feel.
Nils Frahm - Familiar Like Olafur, he is very ecletic in his style, perhaps even more so as some of his stuff is just straight up electronic/ambient and is very unlike contemporary classical. Check out his newest album Spaces and also Felt.
Jonny Greenwood - There Will Be Blood Yes, Jonny Greenwood from Radiohead is a composer, and he composed the soundtrack for one of the greatest films of 00's. There Will Be Blood's soundtrack is just haunting and sinister. Also check out his soundtrack for The Master, another film masterpiece.
Toshio Masuda - Mushishi No Theme The soundtrack of Mushishi is just beautiful and soothing really. It's not exactly contemporary classical and is actually more of world music, but it's really good. In fact, watch the anime, it's beautiful and the music just adds even more to it.
Shiro Sagisu - I'll Go On Lovin' Someone Else I really love the Evangelion soundtracks, the style is diverse from haunting piano pieces to full on dynamic and aggressive full ensemble pieces. Main thing is the music doesn't suck.
Sergei Rachmaninoff - Piano Concerto No. 2 Probably my favourite piece of classical music ever. It's been haunting me from since I first heard it long ago. Rachmaninoff just bring Romanticism to the next level, even more so than any of his Soviet era composing peers. The piano and the wave of the orchestra behind just play off each other so well, definitely his magnum opus.
Maurice Ravel - Jeux D'eau Haunting solo piano piece. Ravel mixes in elements of Jazz into his classical piano, and the results are quite astounding. Really different from the old pre 1900's classical music. Check out his other stuff like Piano Concerto in G Major.