Simply by checking List of ATP number 1 ranked singles players at Wikipedia I found two players who were Year-end No. 1 without winning a Grand Slam tournament that year:
(Connors won his first GS title in 1974 and McEnroe in 1979. But they did not won any GS in the years listed above. Note that McEnroe did not start at French Open and Australian Open in that year. So did Connors in 1977. In 1975 Connor did not play French Open.)
The same Wikipedia article also mentions two players who were at No. 1 position without GS title: Marcelo Rios and Ivan Lendl. (Lendl won several Grand Slam tournaments later.)
This article also says that: Federer could become the oldest Number 1 player since André Agassi. He could also become the third player to end the year in Number 1 position without winning a Grand Slam title after Jimmy Connors in 1975 and 1977 and John McEnroe in 1982.
By checking similar list for WTA Tour on Wikipedia we can find the following year-end No. 1's without GS in the same year
Note that Jankovic and Wozniacki still have not won a GS tournament. (Seles won her first GS title in 1990, Hingis in 1997 and Davenport in 1998.)
It is also worth mentioning 1995 was the comeback year for Monika Seles after the stabbing incident and she only played one GS tournament (US Open). She is listed as year-end No. 1 by WTA together with Steffi Graf (despite having less points than her).
The same Wikipedia article lists 5 players that were ranked No. 1 without having a GS title at the time: Kim Clijsters, Amélie Mauresmo, Jelena Jankovic, Dinara Safina and Caroline Wozniacki. (Clijster and Mauresmo won several GS tournaments, but only after they became No. 1 for the first time.)
This blog post discusses slamless No.1's since 2000.