I had a cat die after a neutering operation - he had a blood clotting problem and the wounds wouldn't stop bleeding. Incredibly rare and desperately sad but I would never avoid having a cat neutered or spayed because of fear on my part about the outcome.
Complications are very rare but if a female cat isn't spayed, she will come into season every 3 - 4 weeks, she may become distressed, her drive to mate will make her determined to get out and 'find some' even if she's a house cat and of course any local entire males will hang around the house.
Plus, as Mollie says, there is an increased likelihood of some cancers in a female cat that doesn't breed.
There are cat contraceptives but unless there is a diagnosed medical problem that makes an operation unfeasible, they're not recommended long-term because they lead to an increased risk of cancers. Also, if a cat vomits within 20 minutes of being given the pill (every 15 days for one that is used in France) the drug isn't absorbed and the cat can conceive.
I am still terribly sad about the loss of my kitten 20 years ago but it has never prevented me getting subsequent cats (there have been a few!) 'done'. Yes, I am always tense on the day of the op but I would not let my fears stop me doing something for the benefit of the animal.