After viewing answers to "Does neutering have any negative effect on the health of a dog?" and "Can a dog contract a sexually transmitted infection?", I am curious to know if there is a trusted way to prevent my dog from mating without neutering/spaying him/her?
Well, yes. For male dogs there is a technique (now FDA approved) called "Zeutering" or zinc neutering that uses chemical compounds to effectively neuter a male dog without surgical removal of the testes. As the article noted, the long-term effects are still being studied and the dog must be quite young.
You might also look at Tardac, which is basically another form of chemical neutering for male dogs, but the effects only last about 3 months and then you have to do it again. Considering the expense, I would probably treat that as a short-term measure for a specific reason.
On humans the two surguries used are called Vasectomy for males and tubal ligation for females. These surgeries can and have been done on dogs, they are clearly effective in stopping pregnancy, though there is some risk (in humans or dogs) of the tube reconnecting.
In Tubal ligation a female's Fallopian tubes are surgically altered so that the egg can not reach the uterus. In Vasectomy a male's vasa deferentia are surgically altered to prevent the sperm from being ejaculated. In both cases the products of reproduction (eggs & sperm) continue to be produced but are not allowed to complete the reproductive path, so they are adsorbed by the body.
These surgeries tend to be a bit more expensive, and are not available in all areas. Some areas that have legal sterilization requirements (spay/neuter) do not recognize the surgical interruption methods. But these surgeries will only prevent conception, and are not 100% effective at that.
As pointed out in comments; this and any surgery that leaves a penis and/or vagina intact will not prevent "mating behavior" from occurring where there are two animals present. Physical separation without the possibility of interaction is the only possible method of stopping all "mating behavior". There multiple problems in actually making this work, both realistic and psychological.