I googled and found the first three not-so-easy ones. I knew the Mark Spitz one, but that's all I knew!

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1. The most successful horse was the Soviets' Absent, who was ridden to four medals (a gold, a silver and two bronzes) over three different Games - 1960, 1964 and 1968.

http://news.bbc.co.uk/solpda/ukfs_sport/hi/newsid_3899000/3899435.stm/

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2. Paul Smart and Hilary H. Smart - Mr. Smart competed at the 1948 Olympics, where he won a gold medal in sailing as skipper of Hilarius, in the Star class. His father, Paul, was his crew. This team is the only father and son to win a gold medal in the same event in the same Olympic games.

http://www.sandybay.org/obits/hilary_smart.shtml

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3. Aladar Gerevich (fencing)
The only athlete ever to win medals at six Olympics, Gerevich is also the only athlete to win the same event six times. In 1952, at age 42, he collected one of each medal at the Helsinki games. In 1956 and 1960 he collected two more gold medals to bring his total medal count to 10. His skills in fencing remain legendary as he competed at the highest levels into his 50s.

http://www.aarpmagazine.org/entertainment/Articles/a2004-05-20-mag-oldathletes.html

I'm a little confused about this last one because I also found this:

Rudolf Kárpáti (1920-2000)
During his outstanding sabre fencing career, he won six Olympic games, of which two victories were gained in individual events. He competed in the colours of Vasas and Budapesti Honvéd. He was of the victorious type, as he only won gold medals in the Olympic Games. He gained the world champion's title in team seven times. In addition to fencing, he was a virtuoso violinist; he completed his violinist studies at the Hungarian Music Academy.

http://www.magyarorszag.hu/angol/orszaginfo/sport/hiressportolok/atletaink_a.html