If two comets come together in space, will they bounce apart, merge into a single body, or could they travel together through space, either touching or orbiting a shared center of gravity?
Yes, binary comets do exist; 8P/Tuttle is an example of one. This is an area that is still being heavily researched, but it is suspected that binary comets can "form from collision, mutual capture, or fission."
In recent news, the comet 67P/Churyumov-Gerasimenko has also been revealed to be a contact-binary by the European Space Agency's Rosetta spacecraft.
If the closing velocity is very low, the energy can be dissipated by the comets squishing. You might consider them to merge into one comet in that case. You might be left with a bunch of pieces all travelling together. Whether you call that one comet, the original two, or many is a matter of terminology-all the stuff will be in the same orbit.