These are all likely to change from day to day but for today anyway:
- symphonies
Schnittke, Bruckner, Simpson, Beethoven, Lutoslawski, Knussen
- operas
I detest all opera that I've heard but I'll go with Wagner because of his influence on pretty much everyone.
- piano pieces (solo)
Beethoven, Debussy, Ligeti, Messiaen, Schnittke, Dallapiccola
- piano pieces (concerto)
Bartok, Lutoslawski, Mozart, Milhaud, Berkeley
- violin pieces
Lutoslawski, Bach, Berg, Ades
- string quartets/quintets
Beethoven, Bartok, Shostakovich, Carter, Simpson, Berg
- chamber music
Messiaen, Martinu, Brahms, Takemitsu
- Vocal music
Schubert, Barber, Berg, Schoenberg, Schnittke
Overall: Beethoven. I know it's the cliched choice but I honestly could've written Beethoven under every heading (except vocal and opera) and it would have been completely justified. I don't think there has been or ever will be a better composer.