There were also , , and . 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.
@Thorondor Tolkien confirmed that Orcs were mammals and would have reproduced like mammals. Sorry if that freaks you out a bit. Either female Orcs stay in the lair to raise their imps or they are hard to tell apart from the males.
@andrewlaubacher The images that just flooded my mind shall never see the light of day.
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.