There is literally dozens of current major leaguers that are sons of former big leaguers and even a third generation family of major leaguers in the Hairstons(Sam-Jerry, Johnny-Jerry Jr. and Scott). Here is a complete list of father/son tandems in baseball history: http://en.wikipedia.org/wiki/List_of_second_generation_Major_League_Baseball_players
There has even been a couple big leaguers who played along with their fathers on the same team. One is Tim Raines Jr and his dad who played together for the Baltimore Orioles in 2001.
The other pair, Ken Griffey Sr. and Jr, did something so unique that it would be difficult to duplicate ever again in baseball. Ken Griffey who already had a distinguished career in the big leagues as a part of three All Star games and winning two World Series titles with the Cincinnati Reds, signed with the Seattle Mariners in August of 1990. When he did this he joined his son who already had been with Seattle since 1989.
On September 14, 1990 against the California Angels history was made. Ken Griffey Sr. came up to bat in the first inning with one runner on and hit a home run over the left centerfield wall off of Kirk McCaskill. Griffey Jr due up next, greeted his dad at the plate and promptly did the same thing-hitting a home run to left centerfield. Thus becoming the only pair of father/sons to hit home runs in the same game and obviously only ones to go back to back.