UPDATE: added headers, more details on picking up at the airport, and how to find the booths
On my travels involving luggage in Japan, I am acutely reminded just how crowded the country can be (and how big the foreigners are in comparison to everyone else). It is nearly impossible to take any non-carryon luggage in the subway or highway buses, and difficult to carry more than one checked baggage on the Shinkansen. Many people utilize various delivery services which can deliver luggage directly to or from an airport.
For airport delivery, you can both send and receive your luggage at the airport.
Sending Airport to Home (or other destination)
When I fly into Narita International Airport, I eventually work my way through customs, and end up on the first floor arrivals lobby. From here, at the end of the large hallway are the booths of various delivery companies (look for signs indicating delivery companies or 荷物宅配サービス). One of the most well-known companies is Kuroneko Yamato, which has the trademark black-cat-on-yellow logo; I have used this company several times. At the booth, you fill out a little delivery form, decide what time the next day you would like your luggage delivered, hand over 1500-2000 yen per bag, and leave the airport much lighter. For much of Kanto (near Tokyo), same day deliveries are possible for luggage received in the morning; next day delivery is standard to most other areas of Japan (some parts of Hokkaido and islands like Okinawa take longer). Now you can proceed lightly to your destination!
Sending to the Airport
Shipping to the airport is a bit more involved and requires more planning, because the bags must be sent two days prior to departure. In my case, I sent my bags on a Thursday for my Monday flight. Collection is also varied; in general you can call a delivery driver to make a pick up at a specific time and place, or you can take your luggage to a store that deals with the delivery company. For Kuroneko, most Seven-Eleven stores are able to send and receive packages and luggage, along with a smattering of other (usually smaller, independent) stores and shops. The forms can be obtained from participating stores before you hand over money and send the bags, which is helpful if you know the store from which you want to send but are unsure of other details (or want some time to pick apart the kanji on the form).
On the airport end, you pick up your luggage in the departures check-in lobby of the appropriate terminal and wing. After that, you can walk across the floor to your appropriate airline check-in station, and only end up carrying all your bags at once for the 5-10 minutes it takes to traverse the huge departures lobby. Also, you can stuff anything into your bags at this time that you forgot/deferred from shipping; for example, toiletries, おみやげ (souvenirs) that you forgot, or evening out the load between checked and carryon luggage.
I have found this service invaluable, especially if you have more than one piece of luggage or are travelling to the airport by bus. Even with the roughly $16-20 per piece of luggage, it is still cheaper to take an overnight bus and pay for luggage than take the shinkansen. Even with the shinkansen, the lightened burden may make your travels more relaxed and stress-free. After a neverending day of travel and a flight covering a dozen timezones, shelling out a few bills is often a very tempting proposition. Since my flight departed at 10:45, I would be traveling through Tokyo around rush hour; the thought of swimming through the sea of commuters with 100lb of deadweight was enough motivation for me to figure out how to ship my bags to the airport.
Yamato Transport (Kuroneko) - Airport Takkyubin (English)