FYI I have the new writeup prepared for when the New Skyliner is launched next month. JRHorse 22:40, 16 June 2010 (EDT)
New "By Train" for Narita Article
Note that an image of the new Keisei Skyliner will replace the one currently shown. I also added another infobox; not sure if this is something that we'd want to get rid of or keep. Also we'll want to edit the article elsewhere to indicate that the train will be a competitive option compared to the bus when traveling between Narita and Haneda airports. JRHorse 09:44, 20 June 2010 (EDT)
The two premier train services that operate out of Narita Airport are the Skyliner and the Narita Express. As a general rule of thumb, Skyliner trains offer the fastest ride into Tokyo, while Narita Express trains offer direct one-seat connections to the bullet trains and most of Tokyo's major train stations.
If you are on a budget and plan to use any of the various commuter train services that run out of Narita Airport, using a stored fare card (Suica or PASMO) will prove to be convenient.
From Narita Airport, the fastest and most expensive way (by rail) into Tokyo is the Japan Railways (JR) Narita Express (N'EX)  into central Tokyo Station. The ride takes 55 minutes, costs ¥2,940 and offers the best connections to Shinkansen (bullet train) services or the JR Yamanote loop line. Trains usually depart Terminal 1 at around 15 and 45 minutes past the hour; there is one hourly departure between 12 Noon and 1 PM, and after 8 PM. Smoking is not permitted on board the Narita Express, and all seats are reserved. Brand new E259-series trains, which offer a smoother and more secure ride, have been introduced on the service from October 2009; they will be fully implemented on all runs by June 2010.
Alternatively, you can continue onward in the same train, which splits in two with the front half heading south to Shinagawa, Musashi-Kosugi, Yokohama and Ofuna, while the rear cars go west to Shibuya, Shinjuku and Ikebukuro. Trains run to Hachioji, Takao and Omiya in the evening, with service from these stations to Narita Airport during morning hours. Reservations are required but can be purchased just before boarding if there is space (and there usually is). If there is no space, JR will sell standing tickets for ¥500 less.
JR East sells a special Suica fare package, called "Suica & N'EX" , exclusively to foreign visitors. The cost includes a discounted fare on the Narita Express (one-way or round-trip, in standard class or green class) and regular JR lines from the airport to any destination in the Tokyo metropolitan area; ¥1500 to use on rail travel in Tokyo or on purchases at locations that accept the Suica card, and a ¥500 deposit. The "Suica & N'EX" card is sold only at Narita Airport, and can be purchased using cash or credit card. It can also be recharged with additional funds, but only by paying cash. The one-way Suica & N'EX ticket is ¥3500 in standard class and ¥5000 for the green car. The round-trip ticket costs ¥5500 in standard class and ¥8000 for the green car; the return trip to Narita Airport must be taken within 14 days and seat reservations must be made prior to departure. (As an example, under this plan a one-way trip on the Narita Express from the airport to Shinjuku in standard class would cost only ¥1500, compared to the normal fare of ¥3110. A round-trip for the same journey would cost ¥3500, compared to ¥6220.)
JR also operates Rapid trains on the Sobu/Narita line, leaving once per hour and stopping at various points along the way, including Chiba. To Tokyo the trip is approximately 82 minutes and costs ¥1,280. These are normal, non-smoking commuter trains and often get crowded during rush hour (though boarding at Narita Airport should not be a problem).
If you have a voucher for a JR pass, then you should exchange it here at the JR View Plaza Travel Service Center (Regular JR ticket counter when the View Plaza is closed), as the Narita Express is free with a Japan Rail Pass. You can also make onward reservations from Tokyo.
The private Keisei (京成, stylized as K'SEI) Railway offers trains to central and southern Tokyo, as well as direct commuter trains to Haneda airport. Keisei trains run on two routes: the faster, more-direct Narita Sky Access Line and the slower, less-direct Keisei Main Line. Both routes connect to Tokyo's Keisei Ueno and Nippori stations. Nippori offers the easiest connection to the JR Yamanote and Joban Lines, and to the Nippori-Toneri Liner for Tokyo's Adachi Ward. At Keisei Ueno you can walk over to JR Ueno station to connect to the JR Tohoku and Takasaki lines and northbound Shinkansen trains, as well as the Ginza and Hanzomon subway lines.
Because the Sky Access and Keisei Main Lines operate on different fare structures, separate ticket gates and platforms are used at Narita Airport's two train stations. Sky Access Line passengers only have to pass through one ticket gate, while Keisei Main Line passengers must pass through two ticket gates.
Sky Access Line
The budget option along the Sky Access Line is the commuter train service known as Access Express, or Access Tokkyu (アクセス特急). Access Tokkyu trains depart every 40 minutes, and most of them run into the Toei Asakusa Subway Line. Making limited stops, the Access Tokkyu is the best way to reach Asakusa (65 minutes, ¥1240) and Nihombashi (70 minutes, ¥1280). Shimbashi (75 minutes, ¥1280) puts you within easy reach of the Yurikamome to Odaiba. A change of trains at Nihombashi will allow you to make a quick hop into the Ginza district (Higashi-Ginza Station, 80 minutes, ¥1280). Many services also continue onto the Keikyu Line for Shinagawa (85 minutes, ¥1460) and Haneda Airport (105 minutes, ¥1740); if your train terminates at Nishi-Magome then you can change trains at Sengakuji station.
After 4:00 PM (5:00 PM on weekends), Access Tokkyu trains run directly into Nippori and Keisei Ueno in 60 minutes at a cost of ¥1200, otherwise you will have to change trains at Aoto station; this increases travel time to 70-80 minutes.
From the Access Tokkyu trains you can transfer at Imba-Nihon-Idai station - two stations after Terminal 2 - to local Hokuso Railway services. At Shin-Kamagaya station you can change to the Tobu Noda Line and Shin-Keisei Railway, and at Higashi-Matsudo station you can change to the JR Musashino Line.
Keisei Main Line
Regular Tokkyu (特急) commuter trains - those that do not carry the "Access" designation - depart from Narita Airport every 20 minutes, reaching Keisei Ueno in 80 minutes at a cost of ¥1000. During the morning and early afternoon hours, you should use these Tokkyu services over Sky Access trains as they offer a one-seat, cheaper ride. After 4:00 PM (5:00 PM on Weekends), Sky Access trains offer a one-seat ride from Narita Airport directly to Nippori and Ueno; the 20 minutes you'll save on the Sky Access train is worth paying the extra ¥200.
If you want to pay more for a reserved seat, Keisei operates hourly City Liner trains during the middle of the day only. Using older trains that operated Skyliner services prior to their upgrade in July 2010, City Liners run on the Keisei Main Line and make stops at Keisei Narita, Funabashi, Aoto, Nippori and Ueno stations. The travel time from Ueno to Narita Airport is 75 minutes at a cost ¥1920. There is also a daily 7:00 AM City Liner departure from Keisei Ueno to Narita Airport. The City Liner is good for traveling to/from Aoto, Funabashi and Keisei Narita stations, otherwise to reach Narita Airport you might want to think about paying the extra ¥480 to use the faster Skyliner.
Other reserved-seat services include the Morning Liner which operates from the airport to Ueno twice in the morning, and the Evening Liner which operates from Ueno to the airport six times at night after the final Skyliner service has run. Morning and Evening liner trains are cheaper than the City Liner at ¥1400, but the drawback is that you can only make a seat reservation on the day of departure from a special ticket vending machine.
From the Keisei Main Line you have the option of transferring at Funabashi station to the JR Chūō-Sobu line or at Katsutadai station to the Tōyō Rapid with through service to the Tōzai subway line, both of which go right through the middle of Tokyo. The Chūō-Sobu line goes through Akihabara (86 minutes from Narita, ¥1100), Ochanomizu, Yotsuya and Shinjuku (104 minutes, ¥1260) and facilitates an easy transfer to the regular JR Chūō express, which goes as far west as Tachikawa, Ōme, Takao and other destinations beyond. The Tōzai line takes a slight southern approach with stops including Kiba (77 minutes, ¥1400), Nihonbashi, Iidabashi and Takadanobaba (98 minutes, ¥1440).
Note that none of the subway or Chūō lines are specifically prepared for travelers with big luggage and tend to get crowded once inside the Yamanote ring, the exchanges at Katsutadai and Funabashi are usually rather pleasant though.