Well, take football for example. A poorly executed tackle(spear), causes the helmet of the tackler to hit the sternum of the person being tackled. This can crack the sternum, bruise the heart, even kill. On the person doing the tackle, it can cause severe brain trauma and spinal damage(due to alignment at impact). This is just one type of injury. Catching someone in the knees can end careers, a firm strike to the spine with a shoulder or helmet, etc.
Mostly it is about protecting the center line(spine, brain, and sternum), imagine a line dividing your body in half vertically. Many of the injuries throughout any sport are located here and of course knees. In football especially, the spine is open for tackles from the back, illegal blocks, accidental spears damaging both parties, etc. Also, you have to consider the fact that in football there are pile ups, blocks where a twisted knee can get 2 guys laying on it, etc.
In terms of preventing injuries:
1. MMA focuses on striking to the head for KOs, which are given far faster than in boxing, and take a fighter out far quicker than in football. In almost any sport, if you get your bell rung, you take 15 seconds and get back in, unless its REALLY bad. MMA doesnt do that, so they dont allow repeated head trauma.
2. MMA controls any joint damage with ref stoppages or tapouts. In football you cant tap and get the 300 pound guy off of your knee that his weight is hyper extending.(just one example of hundreds).
3. MMA doesnt allow any attacks which may damage the spine, anything to the back of the head/spine is against the rules. Football its encouraged. You are supposed to go for center mass as hard as you can. Tacklers want to throw the biggest hit possible to that area.
There are loads more, but these are the main areas.
Also, somebody mentioned soccer.And I know that one of the waitresses once had a brief fling with a pro soccer player and she is still very much into soccer.
I believe that the stats are similar, even though there is,for example, no tackling in soccer.
Why is soccer more dangerous than MMA?