Assuming you're talking about individuals rather than countries, I've done a fair bit of research into this question.
Because of the spacing of the Olympics every 4 years, it's difficult for athletes in many events to make repeated appearances at the games due to falling from their peak athletic performance. There are many instances of athletes appearing in 3 consecutive Olympics in the same event and winning a medal, but it's harder to find examples of athletes medalling in the same event in 4 or more consecutive games.
That being said, let me introduce you to a fencer named Aladár Gerevich. Early on when I was researching this question I was convinced it would be a multi-way tie between athletes who'd medalled in an event 4 times, until I saw this impressive Olympic résumé:
Gold 1932 Los Angeles Sabre team
Gold 1936 Berlin Sabre team
Bronze 1936 Berlin Sabre individual
Gold 1948 London Sabre team
Gold 1948 London Sabre individual
Gold 1952 Helsinki Sabre team
Silver 1952 Helsinki Sabre individual
Bronze 1952 Helsinki Foil team
Gold 1956 Melbourne Sabre team
Gold 1960 Rome Sabre team
Gerevich is confirmed to be the only Olympian who's medalled in the same event in six different Olympic events: Sabre Team, at the games of 1932, 1936, 1948, 1952, 1956 and 1960. Also of note: all six of these medals were Gold.
For more:
http://en.wikipedia.org/wiki/Alad%C3%A1r_Gerevich
5 medals in the same event:
Edoardo Mangiarotti, Italy
Team Epée
1936 (Gold), 1948 (Silver), 1952 (Gold), 1956 (Gold), 1960 (Gold).
(Not to mention his 4 medals in different years for Team Foil)
Reiner Klimke, Germany
Equestion - Dressage
1964 (Gold), 1968 (Gold), 1976 (Gold), 1984 (Gold), 1988 (Gold)
Pál Kovács, Hungary
Team Sabre
1936 (Gold), 1948 (Gold), 1952 (Gold), 1956 (Gold), 1960 (Gold)
(Well, go figure, he was on the same Sabre team as Gerevich up there, the only difference being that he wasn't around for the 1932 games)
A few notable 4-time event medallists:
Carl Lewis, USA
Long Jump
1984 (Gold), 1988 (Gold), 1992 (Gold), 1996 (Gold)
(Note: He had a shot at 5 straight, as he was 5th in world rankings at long jump in 1980, when the US boycotted the Moscow games)
Jenny Thompson, USA
4 x 100 m Freestyle Relay
1992 (Gold), 1996 (Gold), 2000 (Gold), 2004 (Silver)
4 x 100 m Medley Relay
1992 (Gold), 1996 (Gold), 2000 (Gold), 2004 (Silver)
Birgit Fischer, East Germany / Germany
Kayaking - 500m K4
1988 (Gold), 1992 (Silver), 1992 (Gold), 1996 (Gold), 2004 (Gold)
(Note: This is among 10 medals won in 4 different events at a record 6 different Olympic games, and excludes very real medal chances due to the Eastern Bloc boycott of the 1984 games)
Gert Fredriksson, Sweden
Kayaking - 1000m K1
1948 (Gold), 1952 (Gold), 1956 (Gold), 1960 (Bronze)
Addendum: Al Oerter is the only athlete to win the gold medal in the same event four consecutive times. He won the discus event in 1956, 1960, 1964, and 1968.
2 gold medals.
China (51 gold medals)
China took most gold medals, and USA took the most medals.
Michael Phelps won eight gold medals at the 2008 Olympic Games in Bejing, China. He currently holds the record for the number of gold medals won at any one Olympic games. The prior record holder was Mark Spitz. Spitz won seven gold medals at the Munich, Germany Olympic Games in 1972.
United States (35 gold medals)
USA won the most Medals with 104 and 46 Gold Medals
Canada won 14 gold medals in the 2010 Vancouver games - the record for a single Winter games.
USA with 110 Medals China with 50 gold Medals
The Olympic games were not held in 1916 because of World War I.
The United States won the most gold medals in the 2012 Summer Olympic games in the United Kingdom.
The most gold medals Spain has won at an Olympic Games is 13 at the 1992 Games in Barcelona.
USA-28