One of the most irritating things - my largest pet, in my collection of peeves, if you will of modern games is the non-representation of statistics.
Every intelligence based caster has an intelligence statistic of 20+. Is that because they are all super-geniuses? No. It's because characters are created with point buy, or arrange to taste, and spell saves are based off of your intelligence modifier. Your stats are completely disconnected from your character.
But wait! you say. It's true that certain skills could be modified so that you are less good at those skills. And at low levels, this could actually affect your play experience. But as a by product of the infinite scaling of the d20 system, any skill you aren't putting points into at every level, becomes outclassed as you hit the higher levels.
The advantage of old school "3d6 down the line, statistics are where they stick" is that they authentically describe a real person. If you have an intelligence of 6, this means you are actually retarded, limited in the number of languages you can receive (and in Hackmaster, crippled in your skill acquisition). In 3rd edition, you have a -3 penalty to skill checks based off of intelligence. If you don't cast, this is the only limiting factor easily offset by the expenditure of some skill points.
I think it's a problem for me, because of the 'sameness'. There is no mechanical justification or reason in the more modern games to not pump your intelligence up to 24 if you are playing a wizard. There is no mechanical justification for not sacking your other statistics, (i.e. dump stats). Too much depends on this mechanical advantage (every 2 points in intelligence, making it 5% more likely your spells will work). And due to the default creation options, every wizard is a super-genius, instead of a real person with a variety of abilities.
The same can be found in discussions of characters with MAD or how multiple attribute dependency classes are weaker, because there are fewer 'dump stats'.
Well, I run a 1st edition / Hackmaster game, and let me tell you, there are no dump stats, no matter what your class.
Strength: The most important thing that strength does is carrying capacity. I see everyone focused on the plus to hit, or the extra damage - but the real value of strength comes from what you can carry around. Those few extra points of damage in the best case, might buy you a round of combat. It's very very rare that this has any actual impact upon play or the results thereof - and when it does, the issue of choosing to engage in combat was where the real choice was made. But when encumbrance comes up it always has an effect on play. (How are you going to carry those coins? How long are you afloat? How long can you stand there and beat on someone? How fast can you run again?)
Dexterity: Nothing spectacular here, but who doesn't want a lower armor class, and to hit better with missile weapons. Another critical issue with dexterity is the reaction adjustment. Oh, shit, the party is surprised? Well, you're surprised that much less. Considering surprise is the most dangerous part of an encounter, the most likely way for players to die, this can be critical.
Constitution: Again, having an average constitution is fine, but no one would call it a dump stat. Extra hit points, and increased survival chances from system shocks. Also, this is a major factor in your resistance to disease or alcoholism.
Intelligence: This represents the number of languages it is possible for you to know. This is a critical feature in my games. Also, in Hackmaster, it represents you chance to learn skills. Magic-Users needed this stat to determine the number of spells they could know per level, and their chance to learn spells. I think it's worth pointing out that this statistic allows someone to be an effective magic-user without being 18+. A magic user with an intelligence of 10 can cast spells up to 5th level, and know 7 spells of every level. An intelligence of 13 (above average) is needed to avoid spell failure chance.
Wisdom: This statistic in Hackmaster determines your % chance when you check a skill for that skill to automatically increase. If you're not playing a cleric, high or low values can affect your magical defense adjustment.
Charisma: This is the single most important statistic in old school play. Often derided as useless or without point, called the original dump stat - it is in fact the most crucial. It determines how many henchmen you may have and their loyalty. If you have a 17 in Strength, you may hit 15% more often and do an extra four or five points of damage. If you have a 17 Charisma, you get your attack and then your ten henchmen each get their attacks. Which will have a larger effect on combat?
Again, I point out that these aren't abstract combat statistics as they are in the later editions of the game. The reason I feel that the later editions have statistics that aren't representative of the characters is that the statistics almost exclusively affect combat orientated things. The above numbers do affect many things that affect combat, but not all.
They are representative of the capabilities of the character - who they are as a person.
Interestingly enough, reviewing "Men & Magic" I discover that more text is devoted to the effects of charisma then any other statistic.