By plane
Cambodia has international airports at Phnom Penh and Siem Reap.
Direct flights connect Phnom Penh International Airport  (previously Pochentong International Airport) with China (Guangzhou | Hong Kong | Shanghai), Laos (Vientiane), Malaysia (Kuala Lumpur), Singapore, South Korea (Incheon/Seoul), Taiwan (Taipei), Thailand (Bangkok) and Vietnam (Ho Chi Minh City).
Direct flights connect Siem Reap - Angkor International Airport  with Laos (Pakse | Vientiane), Malaysia (Kuala Lumpur), Singapore, South Korea (Incheon/Seoul), Taiwan (Kaohsiung | Taipei), Thailand (Bangkok | U-Tapao (Sattahip/Pattaya)) and Vietnam (Hanoi | Ho Chi Minh City).
Travellers going specifically to visit the Angkor temple ruins may prefer to use Siem Reap as it's only a few minutes away from the main sites; however as Bangkok Airways has a monopoly on direct flights between Bangkok and Siem Reap, it's a lot cheaper to fly to Phnom Penh and to take the bus (or cross overland from Bangkok).
Low-cost carrier Air Asia has introduced flights from Kuala Lumpur and Bangkok to Phnom Penh and Kuala Lumpur to Siem Reap, while Jetstar Asia  has begun flying from Singapore to Siem Reap and Phnom Penh.
Other airlines operating flights to/from Cambodia include Asiana Airlines, Bangkok Airways, China Southern Airlines, Dragonair, Eva Airways, Korean Air, Lao Airlines, Malaysia Airlines (MAS), Shanghai Airlines, Siem Reap Airways (a subsidiary of Bangkok Airways), SilkAir, Singapore Airlines, Thai Airways International, and Vietnam Airlines.

By road
From Thailand
All six international border crossings are open 7 AM to 8 PM and all have visa-on-arrival facilities at the Cambodian immigration checkpoints.
On the Thai side, there are good sealed roads to all 6 crossings. There are no direct bus services from Thailand that cross the border, but there are buses to all crossings except Chong Sa-Ngam.
On the Cambodian side, more basic and less frequent bus services are available from Poipet and Koh Kong.
-To Siem Reap & Battambang - see the Aranyaprathet and Poipet articles for more details
The busiest land crossing into Cambodia, and the most convenient for onward travel to Siem Reap and the Angkor Archaeological Park. Long the stuff of nightmares, the road has finally been paved all the way from the border to Sieam Reap and Phnom Penh.
-To Koh Kong & Sihanoukville - see the Hat Lek and Koh Kong articles for more details
Take a bus to Trat (transfer in Chanthaburi if necessary) and from there a minibus to the border. After crossing into Cambodia there are two possibilities - the once-daily boat to Sihanoukville (can be unpleasant in adverse weather), or else a minibus or taxi to either Sihanoukville or Phnom Penh.
Those with a yen for adventure can try out the four other international crossings:
-Chong Sa-Ngam, Si Saket Province - Anlong Veng
-Chong Jom, Surin Province - O'Smach
-To Siem Reap- Take the minibus from Surin bus station to the border. Once you cross the border, you are in the middle of nowhere,and there are not currently any buses direct from the border. A taxi can be hired for the 5 hour journey to Siem Reap, most of it very bumpy. However you will get a great and unique insight into rural Cambodian life away from tourist areas. Be warned, this journey can be difficult during the rainy season.
The road from the Chong Sa-Ngam crossing is now sealed and it is a comfortable 2hour taxi ride into Siem Reap. However you should pre-order a taxi in Siem reap to meet you at the border. $40/45
-Ban Pakard, Chanthaburi Province - Phra Prom, near Pailin
-Ban Leam, Chanthaburi Province - Daun Lem, the geographically closest crossing to Battambang

From Vietnam
-Ho Chi Minh City - Phnom Penh
Ticket prices usually range from ~US$8-12. Bus passengers will be asked to vacate the vehicle at both the Vietnamese and Cambodian checkpoints. At this crossing only one passport photo is required for a Cambodian visa.
Mekong Express and MaiLinh Bus companies are the most reliable and reputable businesses operating on this route.
It can be interesting to join a Mekong Delta tour (2-3 days) that travels between the two cities; the total cost is about US$25-35 for three days.
-Ho Chi Minh City - Siem Reap
Mai Linh Taxi Company in Ho Chi Minh City provides bus from Ho Chi Minh City to Siem Reap directly from beginning of 2007. The price is US$18.
-Ho Chi Minh City - Kampong Cham
It is possible to cross at the Trapeang Phlong - Xa Mat border but as of now you have to organise your own transport.
-Pleiku - Banlung
It is now possible to cross the border at O Yadaw near Pleiku. Cambodian visas are available on arrival. You can get a motorbike taxi to the border from Duc Co on the Vietnamese side, but there is no regular transport available on the Cambodian side. It maybe possible to hitch a ride with the border officials, though.
-Xa Xia - Prek Chak
There is a (Cambodian) bus service from Ha Tien in Vietnam (where the ferry from the popular Phu Quoc island docks) to various destinations in Cambodia, including Sihanoukville and Phnom Penh. Cambodian visa on arrival.

From Laos
Voeung Kam, Laos - Dom Kralor, Cambodia
Onward transportation not regularly available. Cambodian visas available, but expect 1$ to 2$ of transaction fees on both sides of the border. Travel agencies on both sides have border crossing packages.

By boat
To/from Laos - There is one border crossing for tourists on the Mekong, a 90 minute speedboat ride north of Stung Treng. The border guards have few opportunities for "alternative" income, and will usually try to make a few extra dollars from scamming tourists.
To/from Thailand - There are no ferry services between Cambodia and Thailand. However it is possible to cross the border from Thailand to Koh Kong on foot, take a 15 minute share taxi or motodop (motorbike taxi) ride, and then proceed to Sihanoukville by ferry from there (or vice-versa).
To/from Vietnam - It's possible to travel between Ho Chi Minh City and Phnom Penh by boat, or by combination of road and boat. Fast boats leave daily from Chau Doc in Vietnam's Mekong Delta and take 5 hours to reach Phnom Penh. Chau Doc is a four hour drive from Ho Chi Minh City. A popular overland route is to make a three day trip, stopping at Can Tho and Chau Doc before taking the boat to Phnom Penh.