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In Japan, there are two systems for counting the years, there is the Western system, and the traditional Japanese system based on the emperor system.  Whenever a new
emperor is enthroned, a new era begins in Japan.  This is not always the case, but recently this is the trend.  The current emperor has regined for 20 years (as of 2008, and his era is the Heisei (平成、へいせい) so 2008 is 平成20年.

When displaying a date, the following convention is usually used:

YY-MM-DD 
平成14年7月30日
2002年7月30日　

Since the Japanese system is based on the current emperor, it is possible that in one year, there can be multiple eras. This happened 20 years ago when Emperor Showa passed away on Januay 7th, 1989.  Technically, the first week of 1989 is Showa 64, and from the second week on, it is Heisai 1.

Here are some eras and periods in Japanese history

縄文 Jomon Period: ??? - 300 BC
弥生 Yayoi Period: 300 BC - 300 AD
古墳 Kofun Period: 300 AD -593
飛鳥 Asuka Period: 593 - 710
奈良 Nara Period: 710 - 794
平安 Heian Period: 794 - 1185
鎌倉 Kamakura Period: 1185 - 1333 
室町 Muromachi Period: 1333 - 1573
桃山 Momoyama Period: 1573 - 1603
江戸 Edo Period: 1603 - 1868
明治 Meiji Period: 1868 - 1912
大正 Taisho Period: 1912 - 1926
昭和 Showa Period: 1926 - 1989
平成 Heisei Period: 1989 - present 

Here is a chart mapping western and japanese years

WESTERN YEAR  JAPANESE YEAR 
2000        平成 Heisei 12 
1999           11 
1998           10 
1997           9 
1996           8 
1995           7 
1994           6 
1993           5 
1992           4 
1991           3 
1990           2 
1989        昭和 showa 64 / 平成 heisei 1 
1988        昭和 showa 63 
1987           62 
1986           61 
1985           60 
1980           55 
1975           50 
1970        昭和 showa 45 
1960        昭和 showa 35 
1950        昭和 showa 25 
1940        昭和 showa 15 
1930        昭和 showa 5 
1920       大正 taisho 8