Get a passport and make sure it's going to remain valid
According to a CNN article, only about 30% of Americans have passports, which is an embarrassingly low percentage compared to the other G10 nations. If you don't have one, don't be embarrassed; it's never too late to get one, and it doesn't take too much effort - all you need is 110 bucks, a couple of passport photos, and the patience to wait a few weeks for it to arrive. (Or pay more and get it quicker.) If you have a passport already, make sure it's got a least 6 months left before the expiration date; many countries will not let you in if you don't.
Find out if you need a visa
Check the US Department of State website for the visa requirements for specific countries you wish to visit. If you're traveling long term, keep in mind the expiration dates on them; there's no sense getting a visa that only lasts 90 days ahead of time if you're not going to arrive until six months after you've left home. If that's the case, remember that there are embassies in other major cities in the world that you can go to for visa applications, closer when you expect to arrive in a visa-requiring country.
Find out if you need vaccinations
Check the Center for Disease Control website for vaccination recommendations for the specific countries you wish to visit. Set up an appointment with your doctor and get them. If you can do this before you quit your job and can take advantage of health benefits, plan accordingly.
Consider travel insurance
Some people opt not to do this, but if you've quit your job and no longer have medical coverage, it might be a good idea - especially if you think you might end up having to get air-lifted off the Everest trail in Nepal because of altitude sickness. Surprisingly, travel insurance can be a lot less expensive than the monthly premiums you pay out of pocket simply by being at home. (For about 200 bucks - less than half of my monthly insurance premium in the USA - I had a multi-month travel policy which covered my $4,000 Everest rescue.) Shop around for what suits your needs. American Express Travel has a travel insurance program that includes medical benefits, albeit on the pricey side. For a less expensive policy, check out World Nomads Travel Insurance, which specializes in medical coverage for long-term travelers, and has been recommended by Lonely Planet, Rough Guides, National Geographic, and BootsnAll.
Get your ATM and credit cards in order
Gone are the days of travelers checks. Sure they're available, but in most parts of the world, they're a bit of a hassle to use, or come with a hefty surcharge. Cash is easier these days; ATMs are in most parts of the developing world now, and are almost always a part of a global network that you're already associated with. (There are exceptions though; I was once in Zambia where all but one available ATM in the country was on the MasterCard/Cirrus network - the rest were on Visa.) With all your ATM and credit cards, make sure you remember to call your company and notify them that you're traveling abroad; the worst thing is to have your cards reported as fraudulent or stolen when "mysterious" charges that are yours come from overseas.
Most, if not all, experienced travelers can agree on this: Pack light! When you travel long-term, you obviously can't pack for your entire stay. Long-term travel is different from a short vacation; you are inevitably and regularly going to do laundry on this trip, so there's no sense trying to bring clothes for the entire time. I usually just pack a week's worth of underwear, a week's worth of socks, two pairs of quick-drying pants (one to wear while I'm washing the other), a few shirts, a quick drying towel, and a few toiletries. And you need not pack everything; remember that despite what you may see on television, you really aren't going to the middle of nowhere; stores exist for basic necessities - as well as plenty of other things - and you can simply get things as needed when you're away. (Plus, you might be surprised about what you can do without.)
Step 6: Go see the world, and have the time of your life!
If you've got this far, you're making your dream a reality! If you're still buying into excuses, please go back to Step 1.
Now quit that job, plan that trip, get your documents in order, pack your bags, board that plane, and travel the world! You won't regret it; it'll be the best decision you've made - that's the general consensus of everyone I know who's taken the leap. And if you're still a little afraid, don't worry; that only means it's going to be good. Hell, it's going to be great as you face your fears, conquer your qualms, meet new people (you're never really alone when if you travel solo), explore new cultures, eat new foods, and learn new things about the world - and yourself.