You paid with your credit card: Notify the credit card company right away. It's within your rights to ask for a refund for any services that were never rendered, as long as you contest the charges within 60 days of the charges' appearing on a statement (and some credit card companies extend this period to 90 days). The more money you've paid way in advance, the less you'll get back. So avoid paying anything but basic deposits very far out.
You paid with cash or a check: Your sole recourse is filing a claim in bankruptcy court. Few businesses file for insolvency, but if they do, you become a creditor and stand a chance of recovering some of your lost funds--just be prepared to wait a while, at least two or three years. It'll help your claim if you have a receipt and if you noted on each check exactly what the payment was for.
The operator was a member of a professional organization: The big three groups--United States Tour Operators Association, National Tour Association, and American Society of Travel Agents--may be able to help you rebook through a different operator (at additional cost). The USTOA has a consumer protection plan requiring members to keep $1 million in reserve so customers can recover at least some of their money.
You bought travel insurance: See if your policy covers "operator default." You may be able to get the insurance company to recoup any losses that the credit card company hasn't already taken care of. If you purchased the insurance policy through the operator, direct your questions to the plan administrator.
You used a travel agent: You have an advocate who can arrange a backup plan. Agents are unlikely to guarantee company solvency, however, and they won't be helpful when it comes to recovering lost money. Sometimes they'll offer restitution to maintain a valuable relationship. While your odds of success are low, you could also try suing the agent in small claims court.
You still want to go on the trip: Contact the NTA even if your outfitter wasn't a member. The organization might match you up with an operator who will be willing to accommodate you, at a discount, on short notice. Also, look closely at your itinerary and approach the individual hotels, airlines, and tour guides directly. Hotels should honor any paid reservations, and airline tickets are valid even if the middleman folds.
You don't want to go: Make those phone calls anyway. You never know who'll take pity on you and refund some or all of your money.
Watch out for these red flags
There's no direct phone number
Only the answering machine picks up
Urgent requests for payment
Few trip specifics
A corporate shake-up
Better Business Bureau complaints