A lot of tabletop games handle this via rolling on Injury tables whenever a player character's HP reaches zero. In many cases like these, losing an eye or a limb will prove a hard lesson to learn and will still noticeably set your character back for the mishap, but it's less a punishment than having them kick the bucket for good. After all, it's hard to roleplay the repercussions when you're dead.

Adding randomness to it doesn't tend to be something that irritates many players if it's clearly established in the rules first; It's only if you [i]add in[/i] randomness where there previously was none that people tend to feel that the cause was unfair. 

Depending on the tone of the campaign, there are times when this is more appropriate and when it's less appropriate. Sometimes, a crippling injury will put even a storied MMA fighter out of a career, and there's not much else they can do aside from turn over a new leaf. Other times, you can go right to the doctor and get yourself patched up just fine, leaving you with just some scars and bruises that make good party talk. Lessons learned the hard way tend not to be forgotten any time soon - but what lessons did you learn from getting your ass beat? Well, that's where the fun of it is, isn't it?