I actually don't remember how long it's been since the last time I had dairy products. As a long-established dairy-defier, I frequently give advice to people who are reducing or eliminating dairy, and I figure it makes sense to have that info all in one place. Last updated 2017-05-22.
Almost all of my preferred creamy/buttery dairy substitutes are nut-based. I've done my best to make non-nut suggestions for those with nut allergies, but I'm not really an expert on that front. In addition, I don't distinguish between products made without dairy and products that are kept free of dairy cross-contamination; if you are extremely sensitive, check labels for warnings about "may contain traces of".
If you're going to go fully dairy-free, I highly recommend investing in two kitchen tools: a high-speed blender and a food processor. Mine are made by Vitamix and Cuisinart respectively, and I don't know what I'd do without them. These tools will let you easily make dairy substitutes that are tastier and usually cheaper than the storebought ones. A less essential but still useful third tool is an ice cream maker, which will let you experiment with sorbets and non-dairy ice creams.
When buying packaged prepared foods, look for the word "parve" or "pareve" under a kosher symbol. Keeping kosher requires separating milk from meat; "parve" means that something contains neither milk nor meat and can therefore be eaten with either. This will save you a lot of time checking ingredient labels for sneaky things like whey in sandwich bread, casein in shredded fake cheese, etc. Note that parve things may still contain eggs, honey, and other non-vegan ingredients.
The Non-Dairy Evolution Cookbook has amazing recipes for butter, cheese, whipped cream, and other dairy substitutes. Throughout this piece, I'll be referring to NDEC recipes. I've read and used a lot of non-dairy cookbooks, and NDEC is by far the best. That said, note that almost all their recipes call for either nuts or soy as a base.
Now, on to the substitutions!
Milk (for drinking, cereal, smoothies, etc.)
This is totally a matter of taste. Quality can vary a lot even within brands; I like Silk chocolate milk if it's in shelf-stable Tetrapaks but not the variety in the refrigerated half-gallon carton. Try a bunch of different store-bought milks and see what you like. I prefer almond milk for cereal and soy or hazelnut milk for drinking. Hazelnut milk can be used to make amazing Nutella-like hot chocolate! You can also make your own nut milks in a high-speed blender. I use the NDEC recipe for almond milk, which is just almond meal (aka almond flour) and water, and it's intensely almondy and delicious. Coconut milk (the sort intended for drinking, not the sort that comes in a can) is the best non-nut non-soy option, in my opinion, but some people prefer rice milk. I do like making my own horchata, and should really try it again now that I have a Vitamix.
Proportions for almond milk: 3.75 c water to 1 packed cup almond meal/flour or 5 oz. blanched almonds
Proportions for almond cream: 4.5 c water to 1 POUND (one full bag) almond meal or blanched almonds
Earth Balance is the standout spreadable butter substitute. There are many varieties, including soy-free. Don't get it confused with Smart Balance margarine, which contains dairy. NDEC has a butter recipe but I haven't tried it yet.
In baking, melted butter can be replaced 1:1 with canola oil or melted REFINED coconut oil. (Unrefined coconut oil tastes like coconut. Refined tastes like nothing.) For butter-like sticks, try Earth Balance sticks, but be warned that they are pre-salted; if you use them, you'll probably want to reduce or omit any salt you usually put in your recipes. Fleischmann's unsalted margarine, which is kosher parve, is reportedly very good for baking, but I'm allergic to another ingredient in it so I can't personally vouch for it. Miyoko's Kitchen makes cultured butter that is phenomenally good, but it's extremely hard to find in stores, and it goes off faster than other vegan butters because of the culturing agents. Soooo good though.
NDEC has an excellent almond cream recipe that substitutes well for heavy cream, including whipping up into schlag. Coconut cream—the thick stuff at the top of a can of coconut milk, not to be confused with pre-sweetened cream of coconut for cocktails—can also be put in coffee or whipped. There does exist canned non-dairy whipped cream, but it's quite hard to find outside of hippie specialty groceries, and it mostly tastes like sweetened air with a hint of plastic.
My four-ingredient vegan recipe is here. You can also use melted non-dairy vanilla ice cream.
My recipe is here. (Contains egg yolks, so not vegan.)
Sour cream and buttermilk
The easy way for making ingredients to use in recipes: add 1 Tbsp cider vinegar per cup of vegan cream to make sour cream; add 1 tsp cider vinegar per cup of vegan milk and let stand 5 minutes to make buttermilk. NDEC also has recipes for sour cream and buttermilk that stand well on their own.
I never liked it, so I couldn't tell you which substitute is best, but NDEC has a recipe and there are a few packaged vegan cream cheese varieties available.
There are many, many soy and coconut and almond yogurts out there. WholeSoy unflavored unsweetened yogurt is the best for cooking, and can be used as a starter if you want to make your own yogurt. I've never been a fan of eating yogurt qua yogurt, but I expect brands etc. are mostly a matter of taste anyway, so try some and see what you like.
Cashew ricotta was one of the first substitute dairy products I ever made, and it was life-changing. Soak raw, unsalted cashews for four hours, pour out the water, put the cashews in your food processor, and drizzle in fresh cold water as you process them until the texture becomes creamy and ricotta-like. Add salt to taste. When I use it for lasagna, I process in fresh basil and nutmeg.
Regal Vegan makes a basil cashew ricotta called Basilicotta that's out of this world. Unfortunately, it goes off very quickly. If you buy it, make sure there's still plenty of time before the expiration date, and use it up as soon as you can.
NDEC has superb recipes for a wide variety of cheeses: some for slicing, some for shredding, some for eating by the fistful. I made NDEC's mozzarella with homemade almond milk and it was incredible; the texture wasn't quite perfect, but it was splendid on pasta and pizza, and yes, it melts! It doesn't get gooey, but next time I might add a bit of xanthan gum to help with that. The cheese melts best in steamy/liquid environments, such as when stirred into a pasta sauce. Under direct heat, it will brown but hold its shape. To get an effect like near-liquid melted mozzarella on pizza or lasagna, I recommend either making the cheese without any carrageenan or shredding pre-made cheese, melting it in the microwave, and pouring it onto the dish. Then bake until browned and bubbly.
Miyoko Schinner's Artisan Vegan Cheese isn't quite as good a cookbook as NDEC, but I do really like her gruyère recipe; it makes killer fondue and croque monsieur. Schinner's recipes frequently call for rejuvelac, which is made by soaking and fermenting grains. It's very easy to mess up rejuvelac and get a jar full of mold. My usual substitute for 1 cup of rejuvelac is 1 capsule (1/8 tsp.) of vegan probiotic powder in 1 cup distilled water (tap water, even filtered, has too much chlorine in it). It's not quite as live-culture-y as rejuvelac but it works well enough.
Cheesemaking does take a bit of time and effort; if you're not up for that, try the many packaged shredded cheese substitutes. Lots of people like tapioca-based Daiya cheeses. My personal favorite packaged vegan mozzarella is Follow Your Heart (the shreds, not the block cheese). But homemade cheese is always the best.
As far as I can tell, there is no such thing as non-nut non-soy vegan cheese. If I were to try to make some, I'd probably make my own rice milk and then try it in a cheese recipe, but I don't know how well it would work without the soy/nut protein.
My preferred brands are Daiya and Amy's, not least because their pizzas are gluten-free. Udi's and Schär pizza crusts are also GF and DF.
Pre-sliced sandwich bread
Stroehmann Dutch Country whole wheat bread is my preferred brand, but any brand that's kosher parve will do.
If a recipe calls for both milk powder and water, replace the water with your preferred non-dairy milk. I haven't tried powdered non-dairy milk but apparently it exists.
I recommend exploring homemade sorbets and granitas before you try tackling homemade non-dairy ice cream. Williams-Sonoma has some good recipes. A Vitamix blender can also be used to turn frozen fruit into frozen desserts; there are instructions for this in the manual.
Once you're ready to make your own ice cream, check out the recipes in Mark Foy's Desserts of Vitality. Almost all of them call for lecithin, an emulsifier that's extremely useful for making smooth, creamy ice cream; you can get liquid or granulated lecithin (and many other useful ingredients, especially for cheesemaking) at Modernist Pantry. Those with soy allergies can look for sunflower lecithin.
For store-bought ice cream, Turtle Mountain brands—Soy Delicious, So Delicious, Purely Delicious, etc.—are consistently excellent. Almond Dream is a lot better than it used to be, and Almond Dream Bites (bonbons) are amazing. In my experience, all coconut-based vegan ice cream tastes basically like coconut, no matter what else it's supposed to taste like, but that works just fine for chocolate, almond, and other flavors that go well with coconut. As a rule I prefer nut-based ice creams over soy-based ice creams, but tastes vary a lot. Try things and see what you like.
Chocolate and sweets
King Arthur Flour sells superb high-end chocolate chips that are dairy-free. A wide variety of vegan and non-dairy chocolates are available. Justin's dark chocolate peanut butter cups are dairy-free but made on shared equipment and some people have reported dairy reactions (they used to be labeled vegan and aren't anymore for this reason). If you miss Mounds bars, try Ocho vegan chocolate coconut bars. Not all dark chocolate is dairy-free! Read labels carefully.
Natural Candy Store is a great resource for *-free sweets. Feed Your Face has amaaaaazing vegan caramels.
Oreos are dairy-free. Many brands of gluten-free cookies are also vegan, but not all (Tate's Bake Shop GF cookies are not DF); my favorite brand is Enjoy Life, especially the gingerbread cookies. Newman's Own cookies are also pretty good. If there's a Jewish bakery near you, gorge happily on all their parve cookies.
Medications and supplements
Back before lactose intolerance and dairy sensitivity became commonly known things, lactose was used as a filler for medications—and still is, because they can't change formulations without going through the FDA approval process all over again. If you regularly take medication, check whether it contains lactose. You may need to change brands/manufacturers (every generic has its own recipe) or get medication compounded at a specialty pharmacy.
As a general rule, tablets often contain lactose; capsules of powder sometimes do; gels and liquids generally don't. Read labels and talk with pharmacists.
Many probiotics are grown on dairy cultures. Culturelle and GNC Ultra 35 are both labeled lactose-free; I'm sensitive to dairy proteins as well as lactose and I haven't had any issues with them.
What did I miss? Is anything unclear? Ask all the questions you like!