Alphecca

It all depends on how complicated you want to get, but some basic spices that can really come in handy are:

Italian seasoning (you can make your own, but why bother?)
Cayenne pepper (gives heat to dishes without the bite of vinegar in hot sauce; not applicable if you hate spiciness, of course)
Nutmeg & cinnamon (mostly for sweet things, though cinnamon can do interesting things for savory stuff, too, add some depth; get whole nutmegs and grate them, them and black pepper are the only spices I bother to do that with, but it makes a huge difference in both cases)
Bay leaves (mostly only if you make many sauces or stews, but also add a surprising amount of richness/depth; you don't notice it until it's not there)
Herb de provence (the only semi-unusual thing on the list, but it's a great French herb mix that can do very interesting things to chicken, sauces, sandwiches, whatever)

I can't think of any more that aren't basically just getting fancy, beyond what most people use to cook (though I'm sure someone else will post something obvious that I missed).

I keep McCormicks Montreal Steak Seasoning for, well, steaks and Lemon Pepper for chicken on hand and go through them pretty quick. I also keep a grinder mixed with sea salt and dried garlic.

Herbs such as basil, rosemary, etc. I buy fresh at the store.

As has been mentioned, cayenne is a must.
If you're into salads at all, dill is imperative for home-made salad dressings; can also be used for making pickled eggs...

Tarragon is good too, either with or instead of the dill in salad dressings; it also goes well with salmon

Cumin, whole if you want to take the time to roast it a bit and grind it, or powdered if you're not that finnicky. Nothing in the world smells as good as sauteeing onions with a bit of cumin thrown in

Rosemary, if you like lamb

Sage, if you like beef and pork; goes will with roasted potatoes too

Paprika - combine with ground cumin and use as a rub for chicken; I put it on popcorn, with garlic powder and salt and pepper...

If you're going to be making stir-fry, I'd recommend a Chinese Five Spice blend.

I'd also recommend Worcestershire Sauce, and some balsamic vinegar - they are both great for marinades and just adding general flavour

Oregano is one of those basics for pasta dishes. The lazy kind where you throw it in with some butter, oregano and a can of tomato paste. ;)

Oregano.

As the old rhyme goes: Parsley, sage, rosemary and thyme... and some other stuff.

Basil
Chile powder, like Ancho and Chipotle. I prefer these to Cayenne for most uses, though I have that too.
Cinnamon, powder and, if you make drinks with it, sticks.
Cumin
Marjoram
Onion, dried
Oregano, both European and if you make chilli a few times a year, Mexican.
Parsley
Rosemary
Sage
Savory
Tarragon
Thyme

Mixes are convenient if you cook a lot of certain types of food, otherwise all the separate herbs are listed above:
Italian mix, typically: basil, marjoram, oregano, rosemary, sage, savory, thyme.

Herbs de Provence mix: typically marjoram, rosemary, savory, thyme

Cumin and Chile powder are needed for good chilli, of course, but also separately in stews, soups and other things. Beans and lentils are nice with these.

The dried onion is great if you find you use a lot of finely diced onion for soups and stews where you do not need to see the onion. So not good for onion soup or to replace pearl onions, but if all you need is the flavor.

Tarragon is good for fish and very nice in eggs. Try scrambled eggs with the tarragon added before cooking, just keep them moist.

Cinnamon is best in stick form when making quantities of hot spiced drinks, like cider or coffee. The powder tends to gunk up a lot into a slimey mess. Gor a single mug or two, powder is fine, but never use it in the coffee maker. It will clog the filter and may overflow.

If you like mulled cider and wine, (and in winter who doesn't?), the mulling spice mix from Williams Sonoma is a good deal and way better than buying it all separately. Cheaper too.

Savory is especially nice, almost a must, with read meat stews and soups, like beef, lamb, venison.

Rosemary is good with some meats and also root vegetables when braised or stewed.

Parsley and thyme are good in many meat and veggie based meals.

Marjoram, which adds a buttery flavor to veggie dishes, especially clear mushroom soup, (no cream).

oregano and basil for mediterranian and tomato based dishes

These are all in addition to salt and black pepper of course.

I was just reading over other suggestions.

Definitely add Bay leaf, most certainly for soups and stews. I buy it in the big jars, and use a lot. Dunno why I forgot that.

As grsing said, I have more than this, but these are the core that can get you through an awful lot of traditional Euro-American cooking.

Asian, and especially Indian cuisine, now that is another subject. A big subject. What was your PHD in again?...

Great other comments. I have no tarragon and had wondered if I was missing out.

My original set of spices was onion powder, garlic powder, chili powder, black pepper, cinnamon. And what I cooked and how kind of showed, but those are musts, unless you always use real onion for the onion flavor (you can buy some Vidalia in season, dice and freeze; a Deb's mom trick we are currently enjoying the fruits of... or roots of, as the case may be), ditto the real garlic, and if you sub your own mix of garlic/cumin/red pepper for chili powder.

Red pepper is my next biggie, and actually took the place of chili powder for me a lot of the time. I use it in almost everything.

Powdered ginger is, well, actually I think it was in my initial set. It may depend what you cook, as it is especially important if you do things like fried rice or other Chinese-style. However, I use it in almost everything, and depending how much and with what, it can either be a disinctly strong or sweet flavor of its own, or it can sit in the background as a flovor enhancer. I use it in spaghetti sauce, for instance, in a less pronounced variation of the role of cinnamon as a moderator.

So that's:
1 - black pepper (I could leave it off as it's probably an assumed thing, like salt)
2 - garlic
3 - onion
4 - red pepper
5 - ginger
6 - chili
7 - cinnamon

If I had to ditch one, probably the onion. If I had to ditch two, probably the chili.

I only own ground mustard for the sake of a particular recipe, and seldom add it to other things, but a little can provide a big, and different, kick. I used a small amount in a many-spice rub for thick prok chops a few weeks ago, as I recall, and that was one of thos impromptu "wish I had a recipe" things. Not a must, but of possible interest early in extending beyond the first, say, dozen.

Cumin is a new arrival and now that I have it I am baffled as to why I never had it before.

Savory and rosemary are favorites, and oregano has many uses, especially if you don't get a generic Italian mix. Those vary, and I have two, which I use regularly, especially one I bought cheap before I got the rack that included the other one. As has been suggested, you might go the way of buying the constituents, and then you can mix in various ways, or emphasize what you like rather than what the maker of the mix chose. Still, a good Italian mix is great if you need that sometimes and don't wish to get carried away.

I have and use paprika sometimes, having learned that not only is it good for more than deviled eggs, and not as tasteless as I always thought, but also it is just a milder form of red pepper. It's pretty optional, but more useful than I realized, and I use it periodically. It's good for imparting a reddish color without overwhelming with a hot pepper flavor.

I haven't played as much with some of the spices, like thyme, for instance.

Sometimes a mix can take the place of something you might not otherwise have on hand. Pumpkin pie spice, for instance, includes cloves.

Anyway, making it a doze, let's say:

8 - cumin
9 - savory
10 - rosemary
11 - Italian seasoning
12 - oregano

This list might change on another day. And should probably include sage, but I don't use that as much now that I use more savory and rosemary for my chicken. Sage works well with them, and is one of the major flavors you'll notice if you eat chicken Rice-a-Roni.

Just a quick digression: if you don't have one already, I'd recommend a crock pot - the *ultimate* Lazy Single Guy's kitchen utensil...

It would be really helpful if we knew what sort of food you like. Italian, Tex-Mex, Thai, Russian, Indian, English (they don't use any, other than case-lots of "Bland,"), or what (other than meat-n-'taters)? Do you like hot, sweet, tart, sour, bland, or just "whatever?" Do you prefer fried, boiled, or baked foods, or just don't care? Do your taste-buds not only not care about the difference between a $8 hi-tech coffee and a 75¢ cuppa-joe, can they not tell the difference? All these can make a big difference in what you might use the most. I have a lot of spices, but the straight spices that I think likely get used the most are (in no particular order):
Rosemary, chipotle pepper, cinnamon, ginger, basil, crushed read pepper flakes, ground cumin, sage, caraway, oregano,

For spice mixes: Cajun, Chinese 5-spice, Italian mix, chili powder, pumpkin-pie spice mix (but not for pies; for coffee), bullion, Johnny's, taco/burrito mix. Ketchup, too. I know, technically it's a condiment, but I still feel like I have to put it in here :-)

For some basic "what for" info you might want on any imaginable spice, check out http://www.penzeys.com/

Browse a cookbook; look at the ingredient list for things that look good. If you start seeing the same things come up regularly, that would be a good place to start.

Oregano
Basil
Terragon
Paprika
Cayenne Pepper
Ground Ginger
Allspice
Cinnamon
Sage
Kosher Salt (it really tastes better)

On second thought, if we're limiting the list to only 10 (and there's no reason to) scratch the Kosher salt (you can live with Morton's), above, and add thyme.