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Comments

Always comment code where it is not typical code repeated in many/all scripts and/or not self-explanatory what the code does.
A comment should either be placed directly above the code :

// My comment
if (something == MY_CONSTANT)

or at code line 61 if this fits more natural in the code :

if (something == MY_CONSTANT)
{
	a = b; // My comment

Whitespace

Do not file source code containing white space in end of line. Generally a no-no.
Do not fill parenthesis with whitespace. Place space in front, not after.

Wrong :

if( attack )
if ( attack )

Correct :

if (attack)

Brackets

We use symmetric brackets. One line blocks does not need brackets

if (attack)
{
	me->DoA();
	me->DoB();
}
else
{
	me->SelectA(); me->SelectB();
}

or

if (attack)
{
	me->DoA();
	me->DoB();
}
else
	me->SelectA();

Loop syntax

Similar to if () blocks, one line statements do not need brackets

for (uint32 i = 0; i < loopEnd; ++i)
{
	DoSomething();
	DoSomethingElse();
}
 
uint32 i = 0;
while (i < 10)
{
	DoSomething();
	DoSomethingElse();
	++i;
}
 
do
{
	DoSomething();
	DoSomethingElse();
	--i;
}
while (i > 0);

Magic numbers vs. Constants

Constants makes code easier to read and does also provide a degree of fail safe.
Wrong :

if (player->GetQuestStatus(10090) == 1)
	me->RemoveFlag(58, 2);

Correct :

if (player->GetQuestStatus(QUEST_BEAT_UP) == QUEST_STATUS_INCOMPLETE)
	me->RemoveFlag(UNIT_FIELD_FLAGS, UNIT_FLAG_NON_ATTACKABLE);

Constants are either set as #define, or most preferred in a enum. If it does not exist, make one.

Enumeration vs. define

It is strongly advised to avoid using #defines for constants, use either a const variable or an enum, if multiple variables can be grouped together
Enums must have a name. Separate constant on different enums depending on their type.
Correct :

enum Spells
{
	SPELL_1 = 23444,
	SPELL_2 = 23233,
	H_SPELL_3 = 28345
};

Standard constant name prefixes

Constant names have standardized prefixes :

Quote

SPELL_ : Spell id
NPC_ : Creature_template.entry
ITEM_ : Item_template.entry
GO_ : Gameobject_template.entry
QUEST_ : Quest_template.entry
SAY_ : Script_texts.entry (yell/normal say)
EMOTE_ : Same as above, just different prefix to clearly see its emote
EQUIP_ : Typically a item id(id from dbc, not _template)
MODEL_ : A creature model
H_XX : Heroic mode prefix (goes before the other prefix) XX is max man amount from mode. (OBSOLETE AS OF PATCH 3.2 WITH SpellDifficulty.dbc)
RAID_XX : Raid mode prefix (goes before the other prefix) XX is max man amount from mode. (OBSOLETE AS OF PATCH 3.2 WITH SpellDifficulty.dbc)
EVENT_ : Event/Encounter identifier for instances
DATA_ : Identifiers in instance used for GUIDs/data not being event/encounter
ACHIEV_ : Achievement id

Correct :

SPELL_ENRAGE 
H_XX_SPELL_ENRAGE 
EVENT_ILLIDAN 
DATA_ILLIDAN 
ACHIEV_OH_NOVOS

Naming of variables and functions

No matter what, DO NOT USE HUNGARIAN NOTATION IN VARIABLE NAMES

for public/protected members or global variables:

uint64 SomeGuid;
uint32 ShadowBoltTimer;
uint8 ShadowBoltCount;
bool IsEnraged;
float HeightData;

for private members:

uint64 _someGuid;
uint32 _mapEntry;
uint8 _count;
bool _isDead;
float _heightData;

Methods are always UpperCamelCase and their parameters in lowerCamelCase, just like local variables

void DoSomething(uint32 someNumber)
{
	uint32 someOtherNumber = 5;
}

Remember to use ' f ' after float values when declaring them to avoid compile warnings

float posX = 234.3456f;

Defining an array of structs:

Position const PosMobs[5] =
{
	{-724.12f, -176.64f, 430.03f, 2.543f},
	{-766.70f, -225.03f, 430.50f, 1.710f},
	{-729.54f, -186.26f, 430.12f, 1.902f},
	{-756.01f, -219.23f, 430.50f, 2.369f},
	{-798.01f, -227.24f, 429.84f ,1.446f},
};

WorldObjects

We are used to defining WorldObjects in this way :

GameObject* go;
Creature* creature;
Item* item;
Player* player;
Unit* unit;

...

Something* obj1;
Something* obj2;

References are defined in a similar way (& must be stuck to the type)

Creature& creature;

Never define Creature* me; in a creature script!
'me' is the pointer to the scripted creature

Defining const variables

const keyword should always go after type name

Player const* player; // player object is constant
Unit* const unit; // pointer to the unit is constant
SpellEntry const* const spell; // both spell and pointer to spell are constant

Static variables

static keyword always should be put as first

static uint32 someVar = 5;
static float const otherVar = 1.0f;

File naming & hierarchy

Further reading

Google C++ Style Guide

Thanks to ScriptDev2 for the original guide.