Some women have only one fallopian tube. Sometimes a tube has to be removed due to infection, endometriosis, or tubal pregnancy, and some women are born with only one. If this is your situation, don't worry too much--you can still get pregnant.
While you always hear that women have two fallopian tubes, some women are born with only one. There are all sorts of genetic differences in our reproductive organs, including size and shape. You really would never know unless you have a problem and diagnostic procedures are done. I knew a woman who had a bicornuate uterus (two-chambers) and only found out when she kept having vague abdominal pain. One of the procedures to figure out why was a hydrosalpingectomy that showed the two chambers. They never did find out the cause of the pain, though!
Other women lose a tube to infection (salpingitis), endometriosis, or a tubal pregnancy. Surgeons may try to clear out an infection, but sometimes that's not possible. A tubal infection will often leak fluid back into the uterus, causing irritation and preventing pregnancy. Removing the affected tube (salpingectomy) may be all a woman needs to get pregnant.
Endometriosis can distort the tubes and cause pain, so the treatment may be removing the affected tube. Likewise, a tubal pregnancy may be treated with methotrexate injected into the sac or else removal of the tube.
After that, how good are pregnancy rates? Multiple studies have shown high natural pregnancy rates after ectopic pregnancy treatment, including salpingectomy. Women who have had ectopic pregnancies have a higher risk of another tubal pregnancy, though. So if the tube is really scarred, it's probably better to remove it.
Since we're only talking about the fallopian tubes, IVF is an option. The tubes are merely the way the eggs and sperm meet up and then the pathway for the embryo to make it to the uterus--IVF shortcuts that trip. While it might not be the most romantic way to conceive, the end result is still a baby!