The Dwarf class as written (Moldvay and Mentzer editions)
Hit Dice: d8 (+3 hp per level after 9th)
Armor: Any; may use shields
Weapons: Any except long bow, two-handed sword
Special abilities: Infravision 60' range, 2 in 6 chance to detect slanting passages, traps, new construction, and shifting walls in underground settings, improved saving throws, bonus languages
Base XP: 2,200 (equivalent to fighter +10%)
Maximum level: 12
Beyond maximum level (Mentzer edition): Advancement in Attack Ranks which improve attack rolls in steps, reaching equivalent of Fighter level 25-27, multiple attacks and combat options for high level fighters, half damage from damage-causing spells and magical effects
A freshly rolled-up dwarf character can do just about everything a human fighter can do, with the exception of using a few large weapons. With racial special abilities and better saving throws, the dwarf is the objectively superior character, at least in terms of game mechanics.
The Dwarf, revised
The dwarf class badly needs some tweaks to make it more than just "Fighter Plus."
The most obvious difference that comes to mind is in size and proportion. A dwarf's short stocky frame is built for endurance, not for speed nor athletic feats. A dwarf's base movement rate is 90'(30'). A dwarf character moves as if his or her encumbrance is one category heavier than it actually is, with a minimum of 30'(10'). Additionally, a dwarf can jump only half as far as a similarly encumbered human character, however high or far that is in your campaign. (I have it on good authority that they do not suffer themselves to be tossed, either.)
Dwarves can't mount steeds larger than a pony or donkey without assistance, and can't comfortably ride a war horse. I've seen this alluded to in a few sources, but so far as I know it's never been codified into an actual rule in classic D&D or its clones, so...here it is.
Those factors, plus the 10% XP penalty of the dwarf class relative to the fighter, differentiates the two enough for my taste. If desired, though, a further handicap can be added which is an outgrowth of dwarves' resistance to magic: A dwarf character could be required to fail a save vs. spells in order for beneficial magical effects, including spells, items, and potions, to have full effect. Making the save halves the duration. (This has no effect on magics whose duration is either instantaneous or permanent, such as a healing spell or gauntlets of ogre power.) This means that the more levels a dwarf character gains, and the more its natural magic resistance tends to counter beneficial magic too.
Unfortunately, the similarity between dwarves and fighters at low levels has been extended at high levels. Rather than allowing the two to grow apart, the official rules just give the dwarf the same suite of new abilities that they give the fighter. I've left a few of the fighter abilities to preserve the dwarf's warrior role in an adventuring party, while expanding upon some other archetypal traits.
Dwarves above 9th level with this option gain 2 hp rather than 3. Level advancement and additional abilities are as follows:
XP Level Notes
270,000 9 Gains ability to sense precious metals within 100', 2 in 6 chance.*
660,000 12 Detection abilities improve to 3 in 6. Smash attack.**790,000 13
1,050,000 15 Metal sense improves to 3 in 6.
1,440,000 18 Magical attacks do 1/2 damage, save for 1/4. Detection improves to 4 in 6.
1,830,000 21 Two attacks per round.
2,220,000 24 Detection improves to 5 in 6.
2,610,000 27 Metal sense improves to 4 in 6.
3,000,000 30 Detection improves to 7 in 8
3,390,000 33 Metal sense improves to 5 in 6.
3,780,000 36 Metal sense improves to 7 in 8.
* The affinity that dwarves feel for precious metals is not merely psychological but physical as well. For the average dwarf this attraction is instinctive and unconscious, but dwarves of name level and above become consciously aware of this "sixth sense." The dwarf must concentrate for a full turn to use the ability, but it cannot be blocked except by magic. Within 5' this detection takes only one round, and the dwarf can distinguish between different kinds of metals and even alloys. Even with only very casual inspection, it's near impossible to fool a high level dwarf with debased coins or other inferior alloys.
** A dwarf wielding a weapon in both hands (including one-handed weapons with long hafts that can be gripped in two hands, like maces and war hammers) can deliver a crushing blow by taking a -4 penalty to the attack roll and a +4 penalty to AC. If the attack hits, the dwarf adds his or her entire Strength score, rather than the Strength adjustment, to the damage rolled. The manuever may be attempted with a weapon wielded one-handed, but only half the Strength score is added to damage. (This is a modified version of the maneuver of the same name in the official Companion Set. Use that iteration instead, if you prefer. Dwarves do NOT receive the other Fighter combat options under these rules.)
I highly prefer the saving throw progression from the Moldvay Basic Rules, which starts dwarves off at values of 10-11-12-13-14 (poison/death ray, magic wands, paralysis/petrification, dragon breath, and rod/staff/spell, respectively) from which JB extrapolates in his B/X Companion, instead of the 8-9-10-13-12 which inexplicably shows up in Cook Expert and persists in the Mentzer edition rules.
With the B/X Companion, just use the numbers provided, with the two bumps after level 12 occurring at levels 18 and 30. If you're using Cook Expert or Mentzer tables, subtract 1 from each category at level 18. At level 30 and above, all saving throw values are 2.
That's it (for now) for dwarves. Next up: The elf class gets a makeover.