My favorite piano concertos are by Bartok. I also like Prokofiev's No. 2, Barber, and Schnittke's concerto for piano and strings. I don't care much for romantic concertos of any kind.
As for violin concertos, Ligeti is probably my favorite. I also enjoy Dutilleux, Henze, Norgard, Berg, Schoenberg. I should give William Schuman's a listen. I'm a big fan of his symphonies.