There were also goblin-men, half-orcs, and half-trolls. Their exact natures aren't well defined, however, so it seems we haven't reached consensus on these matters.
I like to think that they were bred by Saruman with genetics rather than actual sexual reproduction. It eases my conscious.
ok to clarify i mean for the 'good' races
Elves and Men are somewhat related already due to their both being the Children of Ilúvatar. Eru created them to be similar enough to be able to procreate with each other. This would not have been the case with the Dwarves. Hobbits might have been able to have children with Men and/or Elves, but there are no records of such a union in the histories of Middle-earth.