Utterly mind bogglingly brilliant CD for testing bass response is Peter Gabriel's 4th solo album, titled "Peter Gabriel". This is the one with the alien picture on the front, as opposed to the first three Peter Gabriel albums (all titled "Peter Gabriel"), which are nicknamed "Car", "Scratch" and "Melt". The fourth was nicknamed "Security", it being the title in the US.
This was the album which precluded the first WOMAD festival and features a fusion of rock music and African instruments. Couldn't recommend another CD highly enough to be honest; there's remastered versions of the LPs out, but if you can find an original Virgin/Charisma release, then that'd be my pick. Great album too.
Classical - highly depends on the recording and type of music you like, so I'll bow out here. You won't go far wrong checking out some of the Gramophone recommendations though. Personally, I've always liked Bruckner's 7th and some of John Adams work.
Jazz - "Coltrane" John Coltrane (Impulse) and "Mingus Mingus Mingus Mingus Mingus" Charles Mingus (Impulse).