Spices are the hard parts of plants: the seeds, bark, roots, pods. Spices are almost always used dry, and are available either as whole spices (the preferred way) or processed into powders or other forms. Spices can be added at any time, but are most often used early in the cooking process.
Herbs are the soft parts: the leaves, flowers, and stems. Herbs are used either fresh or dried, and sometimes this changes their flavor profile, such as with basil. Dry herbs are added to a dish at any time, but fresh ones should only go in for the last minutes of cooking, or after the dish comes off the fire.
That's the easy part to answer. The second half is more difficult because there are so many variables. The herbs kept by a plain meat & potatoes cook are not the same as those used by somebody who cooks "gourmet." Then there are ethnic considerations. And availability issues (i.e., what can sub for A if it's unavailable or too expensive?).
Last time this question came up I actually counted and I had, at the time, 88 distinct spices, herbs, and blends. Does that make me typical? Probably not. Both by inclination and as part of my job as a cookbook reviewer I have a very global outlook, so perhaps require more herbs and spices than the average. I'd be willing to bet, however, that my Mom never had more than half a dozen at any one time. Just a reflection of different cooking styles.
Your primary dried herbs tend to be thyme, sage, rosemary, oregano. Most casual cooks would include dried basil, but others will mock it. You can go a long way with those herbs and they're certainly what I use the most. Then you'll hit a secondary tier with dill, marjoram tarragon and so on.
Fresh, think parsley, cilantro, basil.
Spices, cumin, coriander, currypowder, cayenne, chili powder, cinnamon, nutmeg, are pretty common.
Once you go asian, spices and herbs tend to take on a different role (as long as you stay out of India) From Vietnam up through Japan, your primary seasonings are liquids. And probably Korea, but I've not cooked enough Korean to say much there. Fish sauce, light soy, dark soy, rice wine, rice vinegar, oyster sauce, hoisin sauce are the primary seasonings.
Cinnamon, Star Anise and 5 spice powder make appearances but you can cook a lot of asian food and never reach for these as spices.
Vietnam uses lots of fresh herbs, but almost like a vegetable.
India is a whole new ballgame and probably the pinnacle of spice use. Plenty to study there and I'm no pro on the topic.
Asia is a big place. Most Japanese use mitsuba, shiso, and daikon sprouts, all of which are known but little used in China, and use shredded daikon as a spice, but would only ever have eaten basil at outings to Italian places, and have no clue what cilantro even is. Thailand on the other extreme distinguishes between a number of types of basil (though three types are dominant). Koreans use sesame leaves. In fact Thais use stuff in such a way that make classification can be a challenge -- for example, are cilantro roots and green, soft cilantro seeds and peppercorns herbs or spices?
China is so large and diverse that, if you want to be accurate about it, it's impossible to say "this is what the Chinese use." Believe it or not there are certain parts of China where soy sauce is *rarely* used -- the Fujian style of cooking uses fish sauce and shrimp paste, western Chinese cooking uses cardamom and cumin which are infrequently seen in other parts of China, and they have herbs in the mountains of Yunnan that are literally unknown outside of the province.
It's really better to just target specific styles. But a very short list of the most common things would probably be garlic, green onion, pepper, star anise, ginger (fresh root), basil, chili peppers (in and of itself a huge topic -- there are 79 varieties in Thailand alone), cinnamon, cloves, shallots, cilantro, szechuan pepper (known as Sanshyo in Japan)...
Five spice powder is not standardized but generally contains cinnamon, szechuan pepper, star anise, cloves, and fennel seed (all powdered of course). If you're so inclined you can actually mix your own out of a well stocked spice rack.
I tried to list the most widely and frequently used but there is just no end to it. Pick a style and run through a few recipes. The Japanese is simpler for ingredients -- the aesthetics of the style has its emphasis on quality and technique -- but might be a good starting point to keep things simpler. Or just start at the deep end on Thai or Vietnamese -- the range runs so wide that chances are you'll really run into nearly everything, or some version of everything.
I also agree with Phatch that Indian is a very different game. The spices and herbs are already a bewildering variety, before you even start combining, processing, and aging/fermenting them into different things altogether. And like China it is large enough that there are huge regional variations.
OnePiece there actually are several Kentuckians on Cheftalk. Almost enough of us that we could have our own subgroup.
As you can see from the above answers, you can go in a lot of directions with herbs and spices. Something that seems to have been left out: salt (which, for purposes of this discussion, can be considered a spice), and black pepper---which certainly is the basic spice in American and French cooking.
BTW, it's considered impolite, nowadays, to use "oriental" when referring to people and foodstuffs. The generic word is "Asian."
What I'd rather do than merely list them, however, is to talk a little about how they are used, and how sometimes there is confusion.
Example of confusion: In the U.S., "cilantro" refers to the aerial parts of the plant, and is thus an herb, but "coriander" refers to the seeds, which makes it a spice. In most of Europe and the Far East, however, "coriander" can refer to any part of the plant. So, when following a recipe, consider the source and make sure you understand what ingredient is being called for. Often it doesn't matter, from a taste point of view. But frequently it does, such as cilantro vs coriander. With these two you're also talking about hallmark flavorings for certain cuisines, so it's important to get it right.
Whenever possible buy whole spices, then grind or otherwise process yourself. Reason for this is that whole spices last two days longer than forever (that simple fact is what made the entire historic spice trade possible) . Preground lose their potency relatively quickly (within a year, in fact) due to heat, light, and oxydation. Do not use your wife's coffee grinder for processing spices!!! Get a separate one dedicated to the purpose. Or go whole hog and get a good mortar and pestle. Often, particularly with seeds, dry toasting just before grinding can intensify the flavors. And sometimes, as with chilies, cooking in a little oil can do the same.
There can be a world of difference between fresh and dried herbs. The classic case is basil, which, when dried, takes on a totally differend flavor profile than when used fresh. And dried parsley is the next best thing to tasteless. So, as you expand your cooking horizons be sure and experiment with herbs in both forms. As a general rule, dried herbs are used in a 1:3 ratio to fresh. That is, in a recipe calling for 1 teaspoon of dried X, substitute 3 teaspoons of fresh.
Virtually every supermarket now sells fresh herbs. Most often, with the exception of the two parsleys and cilantro, they come in those small, expensive clamshell packs. So you might consider growing your own. Just about any herb you're likely to use at this point can be grown in a pot in a windowsill, or in a small patch in the yard.
There have been several conversations about growing herbs over in the Chef's Garden forum, so no need to repeat all that here. Just check the back pages and you'll find them.
If you are drawn to Asian fusion, some basic Thai recipes would be good. It seems that 90% of Asian fusion came out of techniques common in Chinese and Japanese cooking, like steaming, stir frying and deep frying combined with the herbs that are most common in Thailand -- chili, basil, lemongrass, shallots, maybe onion and garlic, and lime (kaffir lime to be authentic, but regular lime will do to start).
Basil can be used raw as garnish for additional flavor and aroma at the table. You can stir fry it into the dish like a vegetable. Even basil seeds are made into a sweet soft drink. Lemongrass is usually cracked and put into soup to add flavor, but the pale, tender parts at the root can be shredded and eaten directly, and stalks of lemongrass can be used as skewers the way rosemary is used in the Mediterranean . Lime is used for the juice and zest but also the leaves.
Chilis, shallots, onion, and garlic -- these you probably already know if you cook.