First off, tea is a fantastic drink on its own. Tea comes in a huge range of surprising, delightful varieties, from delicate Oolong to full-bodied Assam, with a zillion different fragrances and aromas to enjoy. So if you insist on drinking it unaccompanied (unadulterated, if you prefer), there's still plenty to enjoy.
However, what with tea being a popular drink around the world for several millenia (centuries, in more backward parts), people have come up with a whole list of things to infuse along with their tea leaves or bags. These are not so-called "herbal teas" (which aren't tea at all), but rather flavourful additives to put a new twist on the same basic taste. Try them!
I've indicated what goes with hot or cold tea, and black or green. I think oolong goes with whatever black tea goes with (but Oolong dissents and, quite frankly, I probably have to bow to authority on this one). Note well: some of these additions will need a few minutes longer to brew than your tea. Let them brew, or you won't feel the taste.
- Milk. Duh. In India you might get tea made with milk rather than water. In the civilised world (aka Great Britain) tea is water-based, but served with a splash of (cold) milk. For hot black tea only! Yummy. Some Brits will tell you to brew the tea, then pour it over cold milk. Non-dairy creamer or whatever they call it in your area is just marginally edible Tippex and should be avoided at all costs. Frothy cappuccino-machine milk is not an improvement.
- Sugar. One or two teaspoons. Makes your drink, well, sweeter. The chemical non-sugar artificial sweeteners will do if you're on a diet, or diabetic. Green tea requires much less sugar, or none at all (true East Asian style). Brown sugar or any non-standard sugar add variety and interest. Goes well with practically anything else on the list, and takes the edge off many of them (and off some bitter teas). Especially fine with milk (to make an ISO standard cup of tea).
- Honey. Another fine sweetener, and very good for a sore throat. Possibly a German(?) idea.
- Lemon (or lime. Squeeze a few drops, or notch a slice and stick it on the rim of your mug (or glass, if you're going Russian), or drop a wedge or slice in the drink (to get the most out of the aromatic peel). Great for hot or cold tea. Also, takes away the aftertaste of tea made with hard water. Orange or other citrus fruits will also do (the peels, mostly), especially in cold tea. See also: lemon tea.
- Blossoms. Various flowers give tea a delicate, fragrant quality. Jasmine and cherry blossoms are well-known examples, and you can buy tea mixed with them. Gritchka also points out rose petal tea, which is very popular too. One or two flowers/petals per cup should be enough, but this depends on how fragrant the flowers are... When you buy jasmine tea, or whatever, the flowers are usually dried, but fresh ones are actually what provides the best flavour; apparently, the flowers you find in bought jasmine tea are there purely for decoration. The extra aroma might take longer to infuse than the tea base. Wait for a few minutes before discarding (if you discard at all) and drinking. Make sure you're using edible flowers only! See also: jasmine tea.
- Herbs. Tea with various herbs is a Middle Eastern classic (although, to add to the confusion, so is herb-only "tea"). These are equally good for hot and cold tea. Spearmint, verbena, lemon grass, some varieties of sage, and a bitter herb I know only by the Arab (Morrocan?) name "shiba", are all good herbs to add to black or green tea. Oolong says basil is good, too, although I can't bring myself to try. Herbs don't go with milk, ever. Lemon is fine, but frequently overpowering. Mixing herbs is great. The extra aroma might take longer to infuse than the tea base. Wait for a few minutes before discarding (if you discard at all) and drinking. See also: Moroccan Tea.
- Vanilla sugar. Make some vanilla sugar, and use it instead of the regular stuff (in similar amounts). Especially good with milk, too. Adding vanilla essence is similar, but not nearly as nice. This is much better than the vanilla tea you can buy ready-made in teabags, which is usually yucky.
- Spirits. More for you ethanol fans than adorers of camellia sinensis, but still... Some people like a drop of brandy in their tea. I think basically this is just an excuse to imbibe more brandy, but give it a try. Other spirits? I haven't heard of that, but I'm sure you can experiment. Updated: wertperch suggests a drop of whisky (aka whiskey); he swears it's just for the flavour.
- Apple juice. Add concentrate to your black tea, or use hot (diluted) apple juice instead of water to steep the tea in. I think this is a Turkish thing, maybe, as you can get Turkish black tea leaves flavoured with apples. You can also drop chopped fresh apple in your steaming-hot tea and let it infuse. Other fruit juice (e.g. berries) will also do, in particular in cold teas, but don't drown out the tea.
- Jam. This is an old-fashioned Russian notion, I think. You get some nice fruit preserves or jam, and either stir a spoonful or two in your tea, or take a good lick from it before every sip of tea. Nice, but it can get to be a bit like slurping liquid jam. See also: Russian tea.
- Fruit extracts. I've never managed quite to achieve the taste of store-bought fruit teas (real tea, not the fruity infusions on sale everywhere). Black tea is soaked in almond or lychee or cherry extract (essence?), so that brewing it releases a soft, enchanting bouquet. I guess any extract you like will do.
- Spices. Indian (or Indian-inspired) chai is made with (some or all of) cloves, cinnamon, cardamon, nutmeg, ginger (fresh, dried, or ground), black pepper (!) or Szechwan pepper, and allspice. Any of these is very nice with black tea. Chai is traditionally very milky, and sweet, and the tea is cooked, not just infused. If you don't use lots of milk, some of the spices will have to be toned down (the pepper, in particular!). Vanilla is also appropriate. Experiment with any brown spices...
- Rice. Yup, rice. sighmoan says: the Japanese make something called Genmai Cha, which is green tea mixed with roasted brown rice -- it has a flavor reminiscent of popcorn. Not something to put in brewed tea, of course; the tea and rice are steeped together. You can buy it already mixed or buy the puffed rice separately (at health food stores?) and add it yourself to the tea leaves. But Pound Fool objects: buying puffed rice doesn't taste the same as using toasted. It's best to just buy it from a place like the Republic of Tea. See also rice tea.
- Boba. lolaleigh explains: it's a Chinese thing. Giant black tapioca pearls in tea, coffee, or really whatever you may be drinking. See pearl tea and Boba Drinks (but not Boba Fett).
- Oil of Bergamot. Can't believe I forgot this on the first pass. You don't actually add this yourself (at least, I've no idea where to get it), but the nice people at Twinings (or whoever) add it to your tea to make Earl Grey. Scrumptious. Goes naturally with milk and sugar.
Update! Wick knows how to do this: "You could get bergamot seeds and either put them in whole or crack them open and grind the seeds in. That's what I do."
- Yak butter. Never tried this one. But see yak butter tea.
I think that's everything I know about. /msg me if I've left anything out.