Traveling to Angkor Wat
Bangkok to Siem Reap - by plane, by train, by bus, by taxi, and by boat, the choices are varied for this popular trip.
Phnom Penh to Siem Reap - this trip is fairly short but it also has a choice of plane, bus, taxi and boats.
Singapore to Siem Reap - for this distance it obviously makes sense to fly, but the surface route is also available.
Siem Reap - Angkor International Airport (IATA: REP | ICAO: VDSR) is the second largest airport in Cambodia.
The following airlines operate service to/from Angkor International Airport:
AirAsia (Kuala Lumpur), Asiana Airlines (Seoul-Incheon), Bangkok Airways (Bangkok), Cambodia Angkor Air (Ho Chi Minh City, Phnom Penh), China Eastern Airlines (Kunming, Nanning), China Southern Airlines (Guangzhou), Jetstar Asia (Singapore), Korean Air (Seoul-Incheon), Lao Airlines (Luang Prabang), Malaysia Airlines (Kuala Lumpur), Silk Air (Da Nang, Singapore), and Vietnam Airlines (Hanoi, Ho Chi Minh City, Luang Prabang).
The airport is less than 15 minutes from the town centre by taxi ($7) or motodop ($4). If you have an advance booking in a hotel, ask the hotel for a free airport pickup (in one of their tuk-tuks).
There are separate terminals for international and domestic flights. International departure tax is a steep $25, or $13 for children, payable after check-in and before clearing immigration. Note that usually this must be paid in cash because the credit card facility is unreliable, so have cash with you. Domestic departure tax to Phnom Penh is $6.
Phnom Penh Sorya Transport  Capitol Tours, and GST Express operate bus service to/from Siem Reap. Direct buses go to Phnom Penh ($10), Pakse ($30), Don Det in the 4000 Islands region of Laos ($27), Kampong Cham, Soung, Battambang, and Kor Kong. Advance bookings are advisable, and can also be sorted out by most travel agents and guesthouses for a $1-$2 fee. Buses generally leave between 7:00AM and 3:00PM.
From Thailand, the nearest border crossings are at Aranyaprathet/Poipet, 3 hours to the north, and Hat Lek/Koh Kong on the coast. See those articles for information on how to get to and cross the border. As a result of recent road pavings, the roads from these border crossings to Siem Reap are in excellent condition. From Poipet, you can take a taxi (US$25 minimum, 2-3 hours, max 4 passengers) or an overcrowded bus (US$10, 6 hours, leaves when full, not as comfortable).
The best budget option is to catch a Thai government bus to the border at Poi Pet (don't buy from Khao San Road), buy the Cambodian visa directly for $20, then after being stamped into the country find yourself a group of four to catch a reasonably comfortable taxi to Siem Reap ($25-30). This will get you to Siem Reap on time, in comparable comfort without funding scammers.