Rock 'Em Sock 'Em Robots
Introduced in 1966, Rock 'Em Sock 'Em Robots featured a plastic boxing ring with two plastic mechanical robots (one blue, one red) in the middle. Players manipulated the robots with controllers on the side of the ring. They could move the robots forward and back, and left and right, as well as throw punches. If you landed a direct hit on your opponent's jaw, it prompted the robot's head to pop up and you won the game. It was simple enough, but every eight-year-old boy wanted one. That was probably because the game featured robots; anything with robots was cool in the '60s. Mattel reintroduced the game in 1996, but in a much smaller format.
Twister
Milton Bradley introduced Twister in 1964 as "the game that ties you up in knots." Its beauty lay in its simplicity and silliness. It featured a large vinyl mat with four columns of different-colored dots and a cardboard spinner. One player tweaked the spinner, which would indicate where the first player had to place a hand or foot, such "Left hand, blue!" or "Right foot, green!" As each player took a turn, the game lived up its claim -- you were tied into knots. If you fell, you were out of the game. The last player remaining was the winner. The game is still popular in 2011 and available in most toy stores.
The Game of Life
Life was introduce by Hasbro in the early '60s and became an instant hit as a family board game. Players spun the large spinner in the middle of the board and moved their tokens (small plastic cars) the number of spaces indicated. Players could go to college or take on a job right way. They got married and had kids (pegs were pushed into the cars to indicate this), earned (and lost) money, encountered problems and successes. The player who arrived at the end with the most money won -- just like real life. Life is still available at your local toy store, and there are online versions as well.
Trouble
Trouble was introduced by Milton Bradley in the mid-'60s. It's a classic "race" board game as players move their pieces around a board in attempt to be the first to reach the finish line. If your piece is landed on by another player -- trouble! -- you have to go back to the beginning and start over. What made Trouble cool and a little different from other board games is that the dice were contained within a plastic bubble that players pushed (Pop-o-Matic). That would cause the dice to jump and tumble (and also prevented you from losing the dice, a common board game problem). Trouble still survives as of 2011 and is available in several versions, including a "Star Wars" theme.