Every few years, somebody makes the very rational suggestion of eliminating the personal foul limit in basketball. Critics inevitably complain that this will lead to more fouling, a more physical game, more injuries, etc. These critics are idiots.
There are many other ways to discourage fouling without throwing players out of the game. The most obvious is to escalate the penalties for fouls, as is done (to a lesser extent) today. For example, you can increase the number of foul shots, give the fouled team shots and possession, make the points automatic (like goal-tending), and so on. Moreover, you can condition penalties on the violence of a foul (as they do on occasion today).
The morons who worry about this escalating game violence ignore the deleterious effects of the current rules. Today, if a key player gets in foul trouble, it is accepted by everyone that the other team should try to drive the ball on him to try to foul him out of the game. To avoid this kind of sick incentive, it is important that the escalating foul penalties be based on team foul counts, not counts for individuals.
Take a look at Naismith's original rules for basketball. While he specifies personal fouls, there is no fouling out, unless a referee judges the foul was made with an intent to injure. (Actually, there were no foul shots. On the second foul, the fouling team lost the player until the next basket, sort of like water polo. I think it would be kind of cool. Also, think of how the power play spices up hockey.)