I did a small study on JR pass. I hope you will find it helpful when you plan a trip around Japan.

JR gorup companies dominate the long haul traffic in Japan. JR pass costs you 28.3 K yen for seven day and 45.1K yen for 14 day use. The cost of a round trip between Tokyo and Osaka is about 28K, one way 14K. So it will give you a general idea of cost comparison. Also bear in mind that limited express ride between Narita and Tokyo or Kankuu and Osaka/Kyoto will cost you more than 3K, they put additional surcharge on these services, fairly expensive but JR pass covers this.

You can use JR pass on various trains including Shinkansen, the bullet train system. Only exception, and this is big, is that you are not allowed to use "Nozomi" bullet trains between Tokyo and Osaka. This is the fastest, and most frequent trains between the two cities. If you want use a Nozomi, you have to pay the full fare and surcharges, not the difference from what JR pass covers. JR may change the rule, so keep an eye on it.

In a big city, there are several private rail and subway systems that JR pass does not cover. You will find them cheaper, faster, and more convenient, so within a big city, you would not ride more than 1 or 2 K yen worth a day on JR lines. So do not expect a big savings here.

Once you have your itinerary set, calculate the JR train fare for the long distance trips, and see if it is more than the JR pass price. JR web site allows to get the exact total price, but it is all in Japanese. Unless you know exact station names in Kanji, the site will not work. So, here is a rule of thumb.

JR fare and surcharges for express and Shinkansen are distance based, mostly linear, but one or two kink points. Rates bellows are shown at the kink points. They are varied by season, route, where you travel, etc. so the numbers below could vary, say by 5 %. Also they sometime uses artificial distance, so it is very very complicated to get an exact total fare.

Fare
Fare is based on the distance. It costs
4950 yen for 300 km
9030 yen for 600 km
11970 yen for 1000 km
for a trunk line travel. Local lines costs you 3 to 5% more. Fare is grouped in 20 to 40 km segment.

Surcharges
If you want to travel by express, sleeper or shinkansen, you have to pay additional charge. This varies depending on season by several hundred yen.

Shinkansen charge: Hikari-Kodama service
4490 yen for 400 km
8280 yen for 1200 km.
Charge is grouped at every 100 km. So, 301 to 400 km costs you 4490 yen, and 1101 to 1200 km costs you 8280 yen. Non-reserved seat will be 510 yen less. Nozomi service costs several hundreds yen more than Hikari service.

Other limited express
2610yen for 200 km
3340yen for 600 km
3660yen for 601 km and above
for a reserved seat. Charge is grouped at every 100 km.

Sample Distance fare ShinkansenCharge
Tokyo - Odawara----84km----1450---2190
Tokyo - Nagoya----366 km---6090---4490
Tokyo - Kyoto-----514 km---7980---5240
Tokyo - Shinosaka-553 km---8510---5240
Tokyo - Hiroshima 894 km--11340---6710
Tokyo - Hakata---1175 km--13440---8280
Tokyo- Sendai-----352 km---5780---4810

Note: The Sendai route charge is more expensive.

Thanks for your helpful contribution. Just a few points to add:

Nozomi runs throughout Tokaido-Sanyo Shinkansen, between Tokyo and Hakata (in Kyushu). Since the opening of Shinagawa stop for Shinkansen in October, JR Central/West have reduced the frequency of Hikari (on which the pass is valid) from 6 an hour to just 2, but trebled Nozomi from 2 to 6. While the ban on Nozomi applies to other schemes beside JR (not available to residents) like Full Moon Pass (for older couples) and Jipangu Club discount scheme (for senior citizens), there was a lot of complaint at that time and a hope that JR would change the rule, but they've decided not to lift the ban, claming that it would lead to overcrowding on Nozomi, popular with business travellers.

Beside the all-line JR Pass, there are several other passes sold by individual company within JR. On the whole they work in a similar way, except that JR East has a very useful 4-day flexible pass (any 4 days within a month), with youth fare (under 25), and some can be bought after arrival in Japan, on production of passport bearing temporary visa. Details in http://www.japanrailpass.net/ and click individual company logo.

JR Central has introduced some APEX-type fares between Tokyo and Osaka, available to anyone. If you buy at least 7 days in advance, you can get around 20% off, subject to capacity limitations. You have to ask specifically for 'Hayatoku' fare or it won't be offered. No change of reservation allowed.

Thank you for the information. I have a few questions regarding the JR pass: In order to ride the Shinkansen from Tokyo to Kyoto will we have to pay extra? We are debating on whether to get a 7 day pass (we are only going from Tokyo to Kyoto, Nara return and then maybe a side trip to Kamakura, Yokohama etc. Please advise as this whole sur-charge busingss is making my head spin!!!

Domo!

It sure is confusing.
Tokaido/Sanyo Shinkansen (Tokyo-Osaka-Hakata) has three levels of services; namely Nozomi, the fastest; Hikari, slightly slower; and Kodama, local Shinkansen service. JR pass does not cover the Nozomi service.

There are other Shinkansen as well. They run to Nagano, Niigata, Yamagata, Hachinohe from Tokyo. Each one has different services, some runs faster than others, but all are covered by JR pass.

Tokyo-Kyoto return trip by Shinkansen Hikari service costs 26,440 yen. Adding one way Narita-Tokyo NEX ride (about 3,000 yen) and some local rides, JR pass for 7 days will be a good choice.

Hikari takes about 2 hours and 45 minutes while Nozomi service takes 2 and 20 between Tokyo and Kyoto. As mentioned before, JR pass does not cover Nozomi and you have to pay13,520 yen each way (Nozomi is slightly more expensive than Hikari) even when you have a valid JR pass.

The biggest problem is, as Alec says, the frequency of service. Hikari runs every 30 minutes while Nozomi runs every 10 minutes.

Another plus with the JR pass: You can use Shinkansen between Kyoto and Osaka/Kobe area with no additional cost.

JR pass is great for a long distance travel. In a big city however, I would recommend you to purchase Passnet (SF Metro card) /Rainbow card and or IO card. These can be purchased at any station from a vending machine. If you are not sure of how to, just ask any staff. You do not save any, but the convenience beats small savings. Even if you own a JR pass, still buy Passnet in Tokyo area, and Rainbow card in Osaka/Kyoto area if you plan an extensive travel around the city. Here is why:

Although the JR group companies dominate the long haul traffic in Japan, in big cities like Tokyo or Osaka, there are several private rail companies and one or two subway systems. Often you will find them faster, cheaper and more convenient. JR pass does not cover these private lines, a big minus.

Technically you have to buy tickets for every company if your travel involves several companies in sequence. Normally you can buy single ticket that allows you to travel to the end of your trip. You are just to show the ticket at the connecting gate or put it into a slot of an automatic gate, and the ticket will pop up at the other end.

The cost of local train ride within Tokyo or Osaka will depend on the distance; you would expect to pay 0.15K to 0.8K per ride. Within a downtown area, each ride will be around 0.2K yen. So seldom you will spend more than 2K a day as long as you are within a city.

In a big city, it is too much of a hassle to buy correct ticket every time you take a train. For example, 5 companies serve Shinjuku station, it is not easy even for Japanese to find a correct ticketing machine. Here is a suggestion. JR system sells so called IO Card, a pre-paid card of 3,000 and 5,000 yen domination. You put the card into a slot of an automatic gate to enter and exit the platform: the minimum fare is deducted when you enter, and any additional amount due is deducted when you exit. You can use it until the money is gone. At the very end, when the amount left is not sufficient for a trip, you can use it with additional coins to purchase a ticket on a vending machine. You might be able to enter to a platform but may be denied an exit, then look around and you should see a little office by the gates area with a staff. He can take care of you.

A similar system called Passnet in Tokyo and Rainbow card in Osaka/Kyoto/Kobe/Nara is used for subway and private companies. The best part of this is that one card can be used with all subway and private lines except for JR system. Rainbow card can also be used for local bus rides. Passnet or Rainbow card handles cross-company travel as long as it does not include JR. One caution; many subway lines in Tokyo are directly connected to JR lines, convenient for users. The card, either IO or Passnet however, cannot handle this two-lines-in-one trip. You are supposed to buy a single ticket to travel this portion. If this happens to you, go to the office when you exit, and staff will take care of the fare.

These card do not have valid period. As long as some money is left, you can use it.

IO (pronounced: e-o) card is being phased out in favour of Suica (pron. su-i-ka) card. It's a bluetooth card so you only need to hold it close to a sensor at the gate without having to insert it. When the credit runs out you recharge it at a ticket machine. There's a 500 yen deposit when you first buy it (2000 yen incl 500 yen deposit), which will be returned when you surrender it (or keep it for the next trip to Japan - valid 10 years!). You cannot use it to enter Shinkansen platforms or for any long distance travel.
Passnet is a throwaway card. When the money runs out, you just buy another.