+Hit Caps for Bosses

Hit rating and spell hit rating are one of the best ways to increase DPS against raid bosses. As raid bosses are considered level 73, you have a much higher chance of your attacks missing than normal. Additionally, hit rating tends to be a "cheap" stat when gear is itemized, meaning that an equivalent amount of hit rating usually does more for your DPS than the same amount of critical hit rating.

However, eventually you have enough hit rating to never miss the boss, and accumulating more hit rating is unnecessary. This is usually referred to as hitting the "hit rating cap".

Base Spell Miss: 16%
Spell Hit % = spell hit rating / 12.6

Spells actually have a 17% chance to miss, but you cannot eliminate that last 1%, so the effective cap is 16%. This 1% does not apply to physical attacks.

Base Melee Miss (Dual-Wielding): 28%
Base Melee Miss (2H/1H+Shield/Special Attacks): 9%
Base Ranged Miss: 9%
Hit % = hit rating / 15.8

For example, as a paladin wielding a two-handed axe, I need to get 9% worth of hit rating, which is equal to 9 * 15.8 = 142 hit rating, in order to never miss the boss. Hit rating beyond 142 is not useful. After hitting 142 hit rating, I should concentrate on other stats like attack power and critical hit rating to increase my DPS.

For dual-wielding, the 28% miss chance applies to both Main-Hand and Off-Hand weapons. However, special attacks, such as Backstab, only have a 9% miss rate. For most classes though, regular melee damage is a significant portion of your total DPS.

The following is the amount of spell hit rating and hit rating you need to minimize misses for raid boss fights, depending on your class and talents.

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Mage

Base: 202
w/ Elemental Precision (Fire/Frost): 164
w/ Arcane Focus (Arcane): 76

Warlock

Base: 202
w/ Suppression (Affliction): 76

Note that a warlock might still want extra spell hit rating for Shadowbolt, in which case Suppression becomes redundant.

Priest

Base: 202
w/ Shadow Focus (Shadow): 76
w/ Focused Power (Smite, Mind Blast, Mass Dispel): 152
w/ Shadow Focus + Focused Power (Mind Blast): 26

Druid (Spell)

Base: 202
w/ Balance of Power: 152

Shaman (Spell)

Base: 202
w/ Elemental Precision: 126
w/ Nature's Guidance: 164
w/ Elemental Precision + Nature's Guidance: 88

Paladin (Spell)

Base: 202

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Druid (Melee)

Base: 142

Rogue (Dual-Wield)

Base: 442
w/ Precision: 363
w/ Weapon Expertise: 387
w/ Mace Specialization (Maces): 387
w/ Precision + Weapon Expertise: 308
w/ Precision + Mace Specialization (Maces): 308

Rogue (Special Attacks)

Base: 142
w/ Precision: 63
w/ Weapon Expertise: 87
w/ Mace Specialization (Maces): 87
w/ Precision + Weapon Expertise: 8
w/ Precision + Mace Specialization (Maces): 8

Hunter

Base: 142
w/ Surefooted: 95

Shaman (Dual-wield)

Base: 442
w/ Dual Wield Specialization: 348
w/ Nature's Guidance: 395
w/ Dual Wield Specialization + Nature's Guidance: 300

Shaman (Two-Handed/One-Hand + Shield)

Base: 142
w/ Nature's Guidance: 95

Warrior (Dual-wield)

Base: 442
w/ Weapon Mastery: 405
w/ Precision: 395

Warrior (Two-Handed/One-Hand + Shield/Special Attacks)

Base: 142
w/ Weapon Mastery: 105
w/ Precision: 95

Paladin (Melee)

Base: 142
w/ Precision: 95
w/ Weapon Expertise: 87
w/ Precision + Weapon Expertise: 40

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Weapon Skill:

First 5 points (351-355): -9.48 hit rating needed per point of weapon skill
Subsequent points (365+): -1.58 hit rating needed per point of weapon skill

(Note that some talents give you weapon skill, and are already accounted for above.)

Dwarves w/ Guns: -47 or -8 hit rating needed
Humans w/ Swords, Maces: -47 or -8 hit rating needed
Orcs w/ Axes: -47 or -8 hit rating needed
Trolls w/ Bows, Throwing Weapons: -47 or -8 hit rating needed

Note that there are two values listed here. Use the second value if you have a talent that grants you weapon skill. Otherwise, use the first value. This is because the first 5 points of weapon skill are worth six times as much as subsequent points.
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Other Factors

Draenai have an aura that increases the chance to hit for the entire party:

Mage/Priest/Shaman Draenai: -12.6 spell hit rating needed
Hunter/Paladin/Warrior Draenai: -15.8 hit rating needed

Finally, there are a couple spells that reduce the amount of hit rating and spell hit rating required:

Druid Improved Faerie Fire: -47 hit rating needed
Shaman Totem of Wrath: -38 spell hit rating needed

Edit: Updated 2007/08/31 to reflect the newest theories for physical hit rating and weapon skill.