Healthy Eating

-lots of fresh vegetables & fruits (except for root vegetables), in amount and variety
-lots of high-fiber foods
-less meat, if any
-fish is healthy, especially fatty red fish such as salmon (an omega-3 source)
-but this has to be moderated due to the unfortunate risk of heavy metal contamination from eating a lot of fish, and due to the environmental problem of worldwide overfishing
-tea is good, in moderation (green & black), unless the caffeine is interfering with sleep
-dark chocolate is good for you; but it has to be in moderation, since it contains a lot of saturated fat
-carbohydrates (carbs) are probably important and necessary for mental health; low-carb ketotic diets are probably hard on the brain. But it is important to choose complex carbs that are released more gradually into your body. Sprouted whole grain breads are better. White bread or rice is almost like pure sugar, in terms of its rate of digestion into simple carbohydrates. Sugar itself should be cut down substantially (it has addictive properties; once you have gradually weaned sugar from cooking and baking, perhaps to 1/3 or 1/4 of what most recipes recommend, you will enjoy the intrinsic flavour of the baking more, and find the higher-sugar recipes unpleasantly sweet).
-components of the "Mediterranean" diet in which there is abundant use of olive oil, is probably healthy
-eliminate trans-fatty-acids from the diet (e.g. hydrogenated oils, often present in many packaged foods to prolong shelf life -- remember this may prolong the oil's "shelf life" on the inside of your arteries as well).
-there is some evidence that there is an excess of omega-6 fatty acids in the typical North American diet; this can be addressed by reducing use of omega-6 rich oils such as sunflower and corn oils, and instead using oils such as canola. Walnuts and flax are other natural sources of healthier omega-3 oils.
-1 to 2 glasses of wine (125-250 mL) per day may improve health compared to abstainers, and compared to those who drink more. But some individuals may have health problems as a result of drinking even small amounts of alcohol. In this case it is best to abstain.
-drinking water is great, but you really don't have to drink huge amounts. Keep yourself well-hydrated, but you only need to drink if you're thirsty.
-I do encourage people to leave all soft drinks behind -- the sugary ones are obviously bad for you. The ones with artificial sweeteners are probably not great for you either, and are also training you to expect sweetness while you hydrate yourself--this conditioning may exacerbate an unhealthy dependence upon simple carbohydrates and sweets, and cause you to be perceive the simple joy of drinking pure water to be unpleasantly mundane. Also do you really want to financially support the big soft-drink companies, with their expanding presence in children's schools, developing countries (many of whose people are dying from starvation), etc.?
-minimize the use of salt
-high-temperature cooking such as barbecuing adds flavour to food, but may result in higher levels of unhealthy chemicals, so it is probably best to reduce the intake of charred food.
-if you are a vegetarian or have other dietary restrictions, make sure you get an adequate intake of vitamins and minerals. A simple daily vitamin supplement should usually be sufficient. I do not see compelling evidence that "megadose" vitamins are beneficial.
-but there is some evidence that the RDA for vitamin D ought to be higher, perhaps up to 1000 IU per day or more.
-extra calcium supplementation may also be needed for many people on a long-term basis, to maintain bone health

While much of this advice is part of basic general health, I think that basic general health is also beneficial to mental health. And there may possibly be specific direct benefits to mental health from a very healthy diet.

I do qualify the above remarks, by saying that extremely clear, direct evidence linking healthy nutritional habits to improved mental health, is lacking. Much of the evidence is indirect or anecdotal. Many exaggerated claims are made in the advertising found in health-food stores. There are a few small studies looking at specific supplements, such as omega-3 supplements, which show some modest evidence that this can improve mood.

Some useful links:
1) the USDA nutrient database (detailed nutritional data about different foods):
http://www.nal.usda.gov/fnic/foodcomp/search/

2) the Cornell University food psychology page:
http://www.foodpsychology.cornell.edu/

The American Journal of Clinical Nutrition is a good academic journal to browse through, to get a good sense of what is going on in food & nutrition research. You can head to an academic library, and leaf through the past year's issues.

Addendum:

After reading the excellent comment on this entry, I feel compelled to add a few things to what I now recognize has been a very dry and pedantic set of comments:
I forgot to mention that I think food is one of the great joys and pleasures of life!
As with other joys, it is wonderful and healthy to develop and nurture a rich culinary experience.
Not only are food, cooking, and eating sources of sensual pleasure, they are also part of a rich and healthy culture (and a way to introduce oneself to new cultures), a part of a social and community life, and a part of an active intellectual life. It is a delight of human nature that we can start with something basic (e.g. an onion, or a grape), and keep refining it, transforming it, and using it in new ways, until we derive more and more art and pleasure from it. There is something very basic about the meaning of life itself in this kind of dynamic.

So I wholeheartedly endorse the idea of embracing and developing a rich culinary culture as part of healthy living. I do still maintain, however, that every culture ought to be informed by science and evidence, and perhaps adaptations can be made to certain cultural practices if we learn that they are harmful (to ourselves, to others, or to the environment). Sometimes the symbolic or esthetic value of a cultural practice can be preserved while the unhealthy aspects can be minimized.