Just wanted to weigh in on this discussion...
There are some valid points on both sides of this debate. I won't rehash them all since they've already been presented numerous times before. But the simple fact remains: "Below average hit points hurt a PC more than above average hit points help". That is directly out of the
DMG, on page 198.
Hit dice are a representation of a character's potential capacity for withstanding damage. In game terms, it simply represent how much damage you can take before you are defeated. Classes that are expected to take the most damage by engaging the enemies at close range, like fighters, should likewise be expected to have the most hit points to make them effective. Rogues have a knack for avoiding damage and are encouraged to flank opponents rather than face them directly, thus they are not reliant on hit points as their main strength. And spellcasters sacrifice their hit point potential for their awesome spellcasting abilities which serve to protect them better than any other class. Realistically, hit dice are more akin to a class feature than just a character attribute.
So the question now becomes "Why is this class feature randomized when others are not?". Because it is still an attribute, and the most abstract one at that. It encompasses stamina, durability, skill, training, and a host of other ideas and concepts that produce the sum of all it's parts. Regardless of it's potential, however, any hit dice still has a chance of rolling a 1. The only difference is that higher hit dice values have a lower chance of doing so, but it's still significant enough to decrease the value of this class feature. If below average hit points are harmful to a character, then the best method is to simply better the odds to avoid lower results and eliminate the worst results altogether.
With that in mind, I formulated an idea based on a few suggestions from other systems like Iron Heroes and modified it. This method allows for the randomized generation of hit points, but gives the player a firm advantage to ensure that even their worst roll is not debilitating to their characters. It still allows for a less than average roll some of the time, but the net results should always be about or better than average.
Code:
[B]HD New Roll[/B]
D4 1 + 1d3
D6 2 + 1d4
D8 2 + 1d6
D10 2 + 2d4
D12 4 + 2d4
After toying with a few different variations and progressions, this is the one that finally made it into my House Rules. You can come up with your own variations of dice rolls and values, if you like.