Is there any reason to believe ginger or garlic help curing or preventing common cold? I've heard this multiple times suggested as a home remedy. What does the science say?
I haven't been able to find anything useful about ginger, but I've found some publications about garlic and - to make long story short - there is lack of good quality evidence for its effectiveness. Some useful quotes are below.
Studies of exercise, garlic, and homeopathy showed unclear evidence of benefit, whereas those of vitamin D and echinacea showed no evidence of benefit. (...) We did not identify any high-level evidence for garlic or probiotics in the treatment of the common cold.
From "Garlic for the common cold." (2014):
There is insufficient clinical trial evidence regarding the effects of garlic in preventing or treating the common cold. A single trial suggested that garlic may prevent occurrences of the common cold but more studies are needed to validate this finding. Claims of effectiveness appear to rely largely on poor-quality evidence.
From "Garlic in clinical practice: an evidence-based overview." (2013):
Garlic as a preventative or treatment option for the common cold or peripheral arterial occlusive disease or pre-eclampsia and its complications could not be recommended, as only one relatively small trial evaluated the effects separately. (...) Garlic might be effective in some areas of clinical practice, but the evidence levels were low, so further researches should be well designed using rigorous method to avoid potential biases.
There is one newer and more positive clinical study about aged garlic extract (AGE), but this is still only a single trial, "Aged Garlic Extract Modifies Human Immunity." (2016):
(...) although the number of illnesses was not significantly different, the AGE group showed reduced cold and flu severity, with a reduction in the number of symptoms, the number of days participants functioned suboptimally, and the number of work/school days missed. These results suggest that AGE supplementation may enhance immune cell function and may be partly responsible for the reduced severity of colds and flu reported. The results also suggest that the immune system functions well with AGE supplementation, perhaps with less accompanying inflammation.
There seems to be lack of evidence about beneficial effects of ginger on common cold.
According to WebMD (info from Natural Medicines Comprehensive Database), there is insufficient evidence about the effect of ginger on common cold.
The article on National Center of Complementary and Integrative Health does not even mention ginger, while it mentions eventual effects of other herbs and remedies on common cold.