Kayak:  Our current favorite site for researching flights, cars, hotels; free alerts.  
TripIt: Manage frequent flyer programs and travel plans; paid version offers alerts for both reservation changes and price drops. 
AwardWallet: Easy organization of frequent flyer programs and travel plans. 
Tripadvisor:  By far the largest crowd-sourced site, reviews and ratings by real people; lots of timely info, but careful: ratings can be manipulated.
OpenTable: Free restaurant reservation site with reviews
Evernote: Tool for organizing all kinds of information (travel and otherwise) on the web, a computer, iPad/iPod, or by smartphone.  Free and paid versions. 
Skype: Free or very cheap international calls over WiFi network.  Can also use data plan from mobile carrier, but watch data fees.
Google Maps: Map out places of interest, location of hotel, restaurants. For many locations, includes directions, weather and traffic. Saving map info for later use requires a (free) google account. And when you won't have a data connection, use Maplets (app):  A real gift for travelers, it allows you to pre-download Google maps for your destination.

Hipmunk:  Close second to Kayak: their visual flight searches are useful AND pretty. 
Google Flights: New, has some interesting features, but no international flights yet.
Skyscanner:  UK-based, similar to Kayak but has some nice features for flights within Europe. 
HotWire: Travel booking site with "best price" feature.
Priceline: Travel booking site with "name your own price" feature. 
Yapta:  FREE alerts for price drops on travel bookings and minimum frequent-flyer-mile awards, before or after booking, but you have to enter the flight info yourself (unlike Tripit).
Seatguru: Plug in airline and flight number for seat advice and plane features (outlets, WiFi).
Airfarewatchdog: Real humans comb the web for airfare deals; you can sign up for free alerts. 
Autoslash: FREE alerts for price drops on car rental bookings.  
Hotels.com: Lots of great last-minute deals, plus their own loyalty program.
Airbnb:  Rent a place to stay in a private home--from space on a futon to an entire house. Has been wildly successful but also somewhat controversial.  

Frommers: Professional travel guides  
LonelyPlanet: Professional travel guides. Specializes in off-the-beaten track destinations.
National Geographic Traveler: Site of the National Geographic Travel magazine
Oyster: NOT crowd-sourced: Oyster's professionals visit and rate hotels personally. 
CitySearch: Local reviews of restaurants and events.
TimeOut: Local event information for cities worldwide.
Concierge: The website of Condé Nast Traveler magazine. Lots of destination info and ratings.
Travel + Leisure: The website of Travel + Leisure magazine. Lots of destination info and ratings.
Departures: The travel magazine of American Express. Some content is only available to their high-end cardholders.
Andrew Harper's Hideaway Report: Subscription-based travel newsletter for high-end travel, ad-free.
TOWD: Tourism Offices Worldwide Directory: find the official local tourist info websites for your destination.
Plnnr: Only covers a limited selection of cities, but fun to try; based on your criteria (length of trip, interests, activity level), Plnnr instantly generates a tour itinerary!

Time-limited deep discounts on high-end travel options, primarily hotels. They can also be a great info source, as they offer both positive and negative info.  Usually require free membership and an (easily obtainable) invitation.

Jetsetter: affiliated with Gilt.com
RueLaLa: Mostly a fashion site, but has a travel section
Vacationist: Approved by the experts at Travel + Leisure magazine.
Tablethotels:  Hotels only.

Bankrate credit card finder: Helps you find the best credit card that fits your needs. 
Nerdwallet: Ditto above, with a slightly different approach.
Ev'reward: Find reward mile offers for different sites before you shop online. 
FlyerTalk: Up-to-date travel-related loyalty reward programs.
FrequentFlier: Tips and discussion boards for frequent flyer and other loyalty programs. 
The Points Guy:  This guy may care more about using points than anyone else on the planet, and his site is loaded with useful info and links. See especially the Beginner's Guide section. 

Nearly every site on this page also has an app (especially the Essentials, above), and also:

GateGuru: The Swiss army knife of flight apps. Airport info and flight status, security line wait times, airport amenities, and tons of other features.  
Flighttrack and Flighttrack Pro: May be the best flight-tracking app, and integrates with TripIt.  Pro version offers push notifications.
Packing (+TO DO!) and Packing Pro: Two versions of a popular packing app.
FlyersRights.org: What you need to know when you're stranded by the airline. 
Sutro Media Essential Guides: Some of our favorite travel apps   
HearPlanet:  Audio tours for many locations.
AllSubway: Offline (yay!) subway maps for cities on six continents, although perhaps not the speediest. (app only)
SitOrSquat: Global bathroom finder sponsored by Charmin. 
GasBuddy: Find cheap gas near you. 
World Customs: Some invaluable cultural information for international travel.  
The World Clock: Careful, there is also an app simply called "World Clock"; this one edges it out on reviews.  

Food and Wine: Food-oriented magazine with good travel writing and restaurant information.
Chowhound: Food-lovers discussion boards with searchable forums for local recommendations.
Urbanspoon: Restaurant search site.
Zagat: Restaurant search and reviews by real people; only paid version gives ratings. Recently purchased by Google, so watch for changes! 
Foodspotting: Finds nearby restaurants and also dishes, in case you can't wait another minute for chocolate mousse. Also a variety of guides by city and type.Savored: A members-only site that offers 30% off all food and drink at popular US restaurants. 

WiFi Finder: Find free and paid hotspots worldwide.
Boingo: Subscription Wi-Fi hotspot service, works in many locations worldwide (especially airports, hotels). Also works with Gogo Inflight Internet service. 
CellularAbroad: National Geographic's site for renting or buying international phones, SIM cards, etc.
Telestial: Their tagline says it all: "Wireless solutions for travelers."
Xcom Global: Rents wifi hotspots (MiFi) for overseas internet access. 
Apple iPad Camera Connection Kit: Handy $30 gadget that allows you to copy photos to any iPad for viewing and backup while you travel. 

Global Electric and Phone Directory: A bare-bones but information-packed guide to plugging in and communicating anywhere in the world.
Google Translate: Just--wow!  
CDC Travel: The Centers for Disease Control and Prevention's comprehensive health information for travelers.
US State Department Travel Site: Travel alerts and tips for traveling abroad, passport and visas. Also offers Safe Travelers Enrollment Program (S.T.E.P.). 
CIA World Factbook: A huge trove of information about countries and regions of the world from the CIA. 
Rail Europe: Research and book European rail travel. Helps you select the best/cheapest ticket type based on your travel plans.
AutoEurope: Book rental cars (and hotels and flights) worldwide.  Includes useful country-specific driving guides.
Global Entry: U.S. Customs & Border control program speeds approved travelers through immigration/customs.  
American Passport: Passport and visa expediter (commercial site, NOT a US government site),  with FAQs, resources.
Xe: Currency exchange rates worldwide, plus other useful info. Also an app.