Trouble is, where do you sleep? Airside is mostly filled with expensive shops and lounges, none of which have beds.
There are airport hotels, of course, and some of them even offer day rooms (where you can stay for a few hours between flights), but they require you to leave the secured area of the airport and come back, which can be a problem. Actual places to sleep if you're in transit are relatively few. Of the fifty busiest airports in the world by passenger traffic (2009), a grand total of nine airports have something along these lines.
Hartsfield-Jackson Atlanta International Airport (ATL): Minute Suites, Concourse B at Gate B15. 5 rooms, $30 per hour.
(This is the only US airport with one of these, although Minute Suites is building one at Philadelphia International (PHL) (opening March 2011) and there's another outfit that claims they're going to open one in San Francisco (SFO).)
Hong Kong International (HKG): Plaza Premium Lounges, two locations in the Departures Level, Terminal 1: before Gate 1 and after Gate 35. This is a paid premium lounge which offers private, shower-equipped suites. 2 hour shower and nap package, HK$230 (US$30).
Amsterdam Airport Schiphol (AMS): YOTEL™: top level (Lounge 2) above Departures 2, near Pier D. 41 standard (single), 15 premium (double), 1 twin/accessible/family room. Four hour minimum starting at €40 standard and €65 double/twin.
Mercure Schiphol Terminal: top level (Lounge 3) above Departures 3, between Gates E and F. 33 rooms. 8pm to 9am for €80, 10am to 7pm for €70.
(YOTEL at London Heathrow and London Gatwick are landside, but still convenient.)
Dubai International Airport (DXB): Dubai International Hotel: third level, Sheikh Rashid Terminal. 78 deluxe rooms, 6 junior suites, 2 royal suites.
Deluxe single room: US$51/hr from 8pm to 3am and US$41/hr from 4am to 7pm.
Double room US$62/hr 8pm to 3am and US$52/hr 4am to 7pm.
Bangkok Suvarnabhumi Airport (BKK):Louis' Tavern Dayroom & CIP Lounges: Level 4, far end of Concourse G.
Standard Room, single occupancy: 2200 baht for four hours; double occupancy: 2400 baht for four hours; additional two hour blocks 1000 baht.
Superior Room, single occupancy: 2400 baht for four hours; double occupancy: 2600 baht for four hours; additional two hour blocks 1100 baht.
Suite Room, single occupancy: 3600 baht for four hours; double occupancy: 3800 baht for four hours; additional two hour blocks 1700 baht.
Singapore Changi International Airport (SIN): Ambassador Transit Hotel: Three locations, one in each main terminal (not in the Budget Terminal):
Terminal 1: Transit Mall East, Level 3. Budget and Standard rooms.
Terminal 2: Transit Mall South, Level 3. Budget and Standard rooms.
Terminal 3: Transit Mall North, Mezzanine Level (Level 3). Standard rooms only.
Minimum 6 hour block: Budget room, single occupancy: S$41.20 nett (including 10% service charge and 7% GST). Standard room, single occupancy: S$68.27 nett. Standard room, double occupancy: $76.51.
(I've actually stayed in a budget room in both Terminal 1 and 2 on separate occasions. They're spartan but convenient, although staff were rather clueless. It looks like management has changed hands since then, so perhaps that's changed.)
Narita International Airport (NRT): Dayrooms & Showers:
Terminal 1: Central Bldg., 3rd Floor. 9 singles, 1 wheelchair compatible, 3 twin, all with shower.
Terminal 2: Main Bldg., 3rd Floor. 8 singles, 3 twin, all with shower.
New (higher) prices starting December 1, 2010:
single ¥1500 first hour, ¥750 each additional hour.
double ¥2400 first hour, ¥1200 each additional.
(I stayed in one of the rooms in Terminal 1 for two or three hours. It was small, but fine for a shower and a nap, which I really appreciated after crossing the Pacific in coach, with another six hours flying ahead of me later that day. This facility is very busy, so getting one of these rooms can be difficult.)
Kuala Lumpur International Airport (KUL): Airside Transit Hotel. Mezzanine Level, Satellite A Building, next to Gate C5. 80 rooms.
Minimum 6 hour block: standard room, queen-sized bed RM140.00 nett
superior room, queen-sized bed RM160.00 nett
deluxe room, king-sized bed RM200.00 nett
suite, king-sized bed RM230.00 nett
Incheon International Airport (ICN): Incheon Airport Transit Hotel. (airport website page) 4th Floor, East Wing (near Gate 11) and West Wing (near Gate 43). 90 rooms.
Standard twin or standard double room: 6 hour block starting at KRW 50,000 for one person, 62,000 for two. 12 hour blocks at KRW 100,000 for one person, 124,000 for two. 16-24 hours charged at 130,000 per person, 140,000 for two.
Deluxe room: 6 hour block KRW 60,000 (1 person) 72,000 (2 persons)
12 hour block KRW 120,000 (1 person) 144,000 (2 persons)
16-24 hours KRW 150,000 (1 person) 160,000 (2 persons)
Suite: 6 hours KRW 90,000 (1 person) 102,000 (2 persons)
12 hours KRW 180,000 (1 person) 200,000 (2 persons)
16-24 hours KRW 190,000 (1 person) 204,000 (2 persons)
Extra hours charged at 8,000 per hour; 4 hours adds a charge up to the next block.
12 hour minimum between 6PM and 7:30AM.
(Renovations are planned for the East facility between the beginning of April and the middle of May, and for the West facility between mid-May and the end of June. During the renovations, each facility will be closed, but presumably the other will be open.)
Delhi Indira Gandhi International Airport (DEL): Eaton Smart New Delhi Airport Transit Hotel (opening 2011) 57 rooms in international wing, 36 rooms in domestic wing; Level 5, Terminal 3. International Terminal hotel opening at the beginning of May 2011. Domestic Terminal hotel opening at the beginning of June 2011.
Sams Snooze At My Space: Opposite Departure Gate 17, Terminal 3. 5 cabins. US$7 per hour.
Zurich Airport (ZRH): Dayrooms and Rest area: Transfer area D.
3 hour minimum block: single CHF 49, double CHF 75, triple CHF 105.
Taiwan Taoyuan International Airport (TPE): Evergreen Transit Hotel. Terminal 2, 4th floor. 11 singles, NT$2,800/night; 6 twins, NT$3,000; 4 triples, NT$3,500.
Colombo Bandaranaike International Airport: The Serendiva Transit Hotel has apparently been completed as part of a recent airport expansion but the facility does not appear to have a web presence. A news article from September 2010 gives some details about the hotel.
Shanghai Pudong International Airport (PVG): there may or may not still be an hourly hotel on the 2nd floor of the transit area, but recent reports say it has closed and there doesn't seem to be a website for it.
All information correct when viewed 11 November 2010 and subject to change.
Of course, if you don't have any money to pay for these options, there's always the guide to sleeping in the public areas of airports.
Edited to add Incheon International Airport's Transit Hotel. Thanks to cityratbuddy.
Edited to add possible closure of Shanghai Pudong International Airport's Hourly Hotel.
Updated 19 February 2011 to add Bangkok Suvarnabhumi Airport's Transit Hotel.
Updated 27 February 2011 to add Delhi Indira Gandhi International Airport's Eaton Smart New Delhi Airport Transit Hotel, and the Sams Snooze At My Space in the same airport. Also added a note about Colombo Bandaranaike International Airport's Serendiva Transit Hotel.
Updated 21 April 2011 to note renovation of Incheon Airport Transit Hotel, and 12 hour minimum from 6PM to 7:30AM.