Nowadays, it seems like it may be nearly impossible to travel with just a single bag that you carry onto the plane with you. Airline regulations have made it so that it's more convenient to check certain innocuous items, like toiletries, than to try to tote them with you. If you can manage it, though, it's great to travel with a single small bag: you're traveling light, you don't have to wait in baggage claim areas, your bags will never be lost somewhere in fair Slovenia.
If you're looking for tips on how to manage this, you don't need to look any further than the redoubtable One Bag website. It's full of travel tips, supply ideas, and packing lists. If you want a slightly different and more basic perspective, check out WikiHow's Travel With One Bag article.
The essence of the One Bag concept is that you make a packing list of only the things you can't do without (nothing you "might need" but aren't sure about). You purchase items that are well-suited for travel: lightweight clothing that doesn't wrinkle and that will dry overnight if washed in your hotel bathroom. You're careful with your money in terms of how you carry it, but you're willing to both buy and discard items when you reach your destination.
The concept is tailor-made for male travelers... and female travelers who are able to subvert or ignore cultural expectations. If you aren't one of those women, though, and you're wondering how single-bag travel can work for you, keep reading after the break!
I don't think the One Bag concept is all that friendly to female travelers, particularly female business travelers. (Actually, the One Bag website seems to be primarily devoted to other kinds of travel: backpackers and adventure travelers will probably get the most out of it.) Nonetheless, adapting it for yourself seems to be all about the choices you make.
There are certain cultural expectations for a "professional appearance" that most women cleave to, even away from home: makeup, carefully styled hair, and so on. Those expectations make it difficult to get everything down to a single bag, even more so when strict airline regulations mean you may not be able to put some of the products you need in a carry-on.
There are ways to make this easier -- like buying slinky-knit, wrinkle-free, travel-friendly clothes from places like TravelSmith -- but a "professional-looking" woman usually needs more real estate in her luggage than a "professional-looking" man, because the look for women takes much more to maintain.
Example: I have waist-length hair. Even if I wear minimal makeup, I still have to travel with a hairbrush, a specific shampoo and conditioner, a few pins and elastics to put my hair up with, and at least one multi-tasking styling product. If I don't, every day I'm on vacation will be a bad hair day.
Travel gurus might suggest that I get a shorter haircut if I plan to make a lot of trips. But except for the conditioners, my long hair is much lower-maintenance than it was when I had an ultra-short pixie cut: I washed it more frequently then, required more styling products, needed to use an electric hair dryer, and often used barrettes. Meanwhile, The Mister shaves his head -- and doesn't even need a comb. C'est la vie.
Another way women can make frequent travel easy on themselves is to invest in a cosmetic palette. Some come pre-made, some are custom items that are made to be filled by their owners (good ones are made by Stila and M.A.C.). The pre-made palettes come in an array of styles and colors, from many companies. They're usually made up of "colors that look good on everyone" (which, in practice, means neutral browns, some with pink tones, often sheer).
Pressed powder cosmetics may be most readily accepted for air travel: you can even use a powder foundation like M.A.C.'s Studio-Fix. However, cream stick cosmetics are another option: one foundation stick, one for lips and cheeks, one or two for eyes. Some sticks will even cover eyes, lips, and cheeks in one. Sticks are probably the easiest cosmetics to transport and apply: they won't shatter if you drop them, and you don't need brushes to apply them.
If you're traveling to a place where you plan to stay for a while, and you can afford it, it probably wouldn't hurt to travel without cosmetics or many hair products. You can make a visit to a drugstore or discount store when you reach your destination, and pick up the basics of what you need there in the smallest sizes you can find. If you're out of your own country, you may enjoy trying local brands.
Another possibility is to give in and check a bag with replaceable things, but keep your bare minimums (toothbrush, toothpaste, comb, sunblock, lip balm, an outfit or two, etc.) in your carry-on... a good idea whether you're attempting One Bag travel or not.