Q:

Which are the sources of a Hide in Plain Sight ability? 

Source can mean anything like an item, feat, class feature, template, magical location, spell, racial trait, domain granted power, etc.  from any official material, such as Drow of the Underdark (non-core), Dragon Magazine (not a book), or Wizards of the Coast (WotC) web articles (not print).  
A Hide in Plain Sight (HiPS) ability means an ability to Hide (even) while being observed AND/OR without having anything to actually hide behind. 
Why I define HiPS as either or both criteria is because, generally speaking, either one sounds like (an ability) to hide in plain sight, and because there doesn't seem to be a prototypical (source of a) HiPS ability.  So instead of any ability that is named "Hide in Plain Sight", I define it by the elements that are most common and popular to a HiPS ability. 
Because there is no prototype, please be detailed about the HiPS ability that each source grants, such as whether it's extraordinary or supernatural, whether it requires shadow, etc..
If there is something similar enough or better, please mention it too. 
Here is an example of several of my points and an example of an answer: 

the Hellbreaker prestige class (Fiendish Codex II: Tyrants of the Nine Hells, p.86) - 1st level

Mantle of Darkness (Ex): You can make Hide checks in any kind of darkness, even when observed by creatures that can see in darkness. 

I want to know because I love the thrill of stealth, so I want to know how to get such a valuable stealthy ability. 
If you think my question should be amended, please let me know and I will try to accommodate you.  

A:

I'll note if the definition says to see another source, but there is disagreement as to what that means. 
Here are the sources of a Hide in Plain Sight (HiPS) (or sufficiently HiPS-like) ability:

the Ranger base class (Player's Handbook, p.46) - 17th level+, extraordinary, even while being observed, natural terrain
the Scout base class (Complete Adventurer, p.10)

(Ex):Beginning at 14th level, a scout can use the Hide skill in natural terrain even while being observed.  See the ranger class feature, page 48 of the Player’s  Handbook.  A  scout loses  this  benefit  when wearing  medium  or  heavy  armor  or  when  carrying  a medium or heavy load. 

the Shadow Shaper Illusionist variant (Unearthed Arcana, p.63) - 15th level, "as the ranger ability, except that the illusionist need not be in natural terrain"
the Wilderness Rogue variant (Unearthed Arcana, p.56) - 13th level (earliest), "as the 17th-level ranger ability"
the Assassin prestige class (Dungeon Master's Guide, p.180) - 8th level, supernatural, even while being observed, within 10 feet of shadow, "can hide himself from view in the open without having anything to actually hide behind.  He cannot, however, hide in his own shadow." 

the Avenger prestige class - ″

the Shadowdancer prestige class (Dungeon Master's Guide, p.194) - 1st level, supernatural, even while being observed, within 10 ft.  of shadow, "can hide herself from view in the open without anything to actually hide behind.  She cannot, however, hide in her own shadow." 
the Dark template (ToM161 ...

(Ex): Use the Hide skill even while being observed (except in natural daylight, the area of a daylight spell, or a similar e[ff]ect). 

the Collar of Umbral Metamorphosis wondrous item (Tome of Magic, p.156) - "transforms you into a [...] dark creature"

... or C:TTotW152)

(Su): Can use the Hide skill while being observed and while lacking cover or concealment, except in natural daylight, the area of a daylight spell, or similar magical light. 

the Failed Shadow Gate magical location (Cormyr: The Tearing of the Weave, p.154) - ultimately "grants a character the dark template"

the Blend into Shadows feat (Drow of the Underdark, p.47)

As a swift action, you can spend a use of your darkness spell-like ability to make a Hide check, even while being observed and without cover or concealment.  You must be within 10 feet of an area of magical darkness. 

the Eye of Lolth prestige class (Drow of the Underdark, p.80)

(Ex): Beginning at 6th level, as long 
  as you are within 10 feet of some sort of a shadow, you can use the Hide skill even when being observed.  See the assassin class feature, DMG181. 

the Hellbreaker prestige class (Fiendish Codex II: Tyrants of the Nine Hells, p.86) - 1st level

Mantle of Darkness (Ex): You can make Hide checks in any kind of darkness, even when observed by creatures that can see in darkness. 

the Dark Lantern prestige class (Five Nations (Eberron), p.69)

(Ex): Beginning at 9th level, you can use the Hide skill even while being observed. 

the Lurking Terror prestige class (Libris Mortis: The Book of Undead, p.54) - unaffected by errata  

(Ex): At 3rd level, a lurking terror can use the Hide skill even while being observed, as long as it has cover or concealment. 

(The rest thanks to Arkhaic)

the Ninja Spy prestige class (Oriental Adventures, p.43) - 4th level, supernatural, within 10 ft.  of shadow, without anything to actually hide behind, not own shadow, unaffected by neither update nor errata
the Wildrunner prestige class (Races of the Wild, p.139) - 5th level, extraordinary, "natural terrain even while being observed", "[s]ee the ranger"
the Stalker of Kharash prestige class (Book of Exalted Deeds, p.75) - 4th level, extraordinary, even while being observed, "[w]ith at least one-quarter cover or one-quarter concealment"
the Justice of Weald and Woe prestige class (Champions of Ruin, p.48) - 9th level, "as the ranger ability"
the Black Dog prestige class (Dragonmarked (Eberron), p.95)

Lost in the Crowd (Ex): From 4th level on, you are able to use the Hide skill while being observed.  As long as at least three creatures larger than you stand within 10 feet in any direction, you can attempt to conceal yourself from view without having cover or concealment. 

the Luiren Marchwarden prestige class (Shining South (Forgotten Realms), p.35) - 5th level, extraordinary, "within the confines of his march"
the Umbral Disciple prestige class (Magic of Incarnum, p.158)

Embrace of Shadow (Su): Starting at 3rd level, you can weave incarnum into an obscuring shadow that clings to you, providing you with a limited amount of concealment.  While you are thus cloaked in shadow, each attack made against you has a 10% miss chance per point of essentia invested in this ability.  This miss chance does not stack with miss chances provided by any other ability or effect. 
  If the miss chance granted by this ability is 20% or higher, you also gain the ability to hide in plain sight—that is, you can use the Hide skill even while being observed.  See the 
  ranger class feature, page 48 of the Player’s Handbook.  Embrace of shadow is usable at will. 

the Shadowcraft Mage prestige class (Races of Stone, p.120)

Cloak of Shadow (Su): A shadowcraft mage can cloak her form in shifting shadows.  This ability provides her with a variable amount of concealment depending on her level.  While her cloak of shadow is active, attacks against a shadowcraft mage have a miss chance equal to 15% + 5% per class level (to a maximum of 40% at 5th level).  Darkvision and low-light vision offer no help in piercing the cloak of shadow, although any creature that can see in magical darkness can ignore the miss chance, as can a creature with true seeing.  A shadowcraft mage can dismiss or resume this effect as a free action.  While her cloak of shadow is active, a shadowcraft mage can make Hide checks as if she had concealment. 
  Cloak of shadow doesn’t function in daylight, and it is the equivalent of a 3rd-level darkness effect for the purpose of interacting with light spells. 

the Nightsong Infiltrator prestige class (Complete Adventurer, p.65) - 10th level, extraordinary, natural terrain, unaffected by errata
the Scar Enforcer prestige class (Races of Destiny, p.130) - 7th level, extraordinary, natural terrain, "[s]ee the ranger class feature"
the Forest Reeve prestige class (Complete Champion, p.82)

Camouflage (Ex): Beginning at 4th level, you can use the Hide skill in any sort of natural terrain, even while being observed. 

the Shadowspy prestige class (Complete Champion, p.105) - 9th level, supernatural, sunlit, unaffected by errata
the Ebonmar Infiltrator prestige class (Cityscape, p.79) - 8th level, extraordinary, natural terrain, "functions like the ranger ability"
the Nightmare Terrain spell (Complete Mage, p.111) - unaffected by errata

Illusion (Shadow)
Level: Assassin 3, bard 3, hexblade 3,
  sorcerer/wizard 4
Components: V, S
Casting Time: 1 standard action
Range: Close (25 ft.  + 5 ft./2 levels)
Area: Five 10-ft.  cubes + one 10-ft. 
  cube/level (S)
Duration: 1 round/level
Saving Throw: Will disbelief (if
  interacted with)
Spell Resistance: No  
You cloak your surroundings with phantasmagoric figures, creating a horrific dreamscape. 
You make any terrain look, sound, and smell like something out of a nightmare. 
  Writhing vegetation, disembodied limbs, animated corpses, and smoking pits cover every surface.  Miasmic vapors fill the air, along with various foul stenches. 
  The nightmare terrain you create is mostly illusory, but the obstacles are partially real.  Creatures within, entering, or viewing the area are entitled to Will saves to discern the illusion.  Creatures that fail their saves become entangled. 
  Regardless of the outcome of the save, creatures within 5 feet have concealment, while those 10 feet or farther away have total concealment. 
  Furthermore, as long as you are within the area of this spell, you can attempt Hide checks even while being observed. ( Other creatures don't gain this benefit.) 

the Know the Shadows spell (Oriental Adventures, p.107) - unaffected by update or errata

Illusion (Glamer)
Level: Shu 2 (Air)
Components: S, DF
Casting Time: 1 action
Range: Personal
Target: You
Duration: 1 minute/level (D)  
You bend surrounding shadows and blend them to yourself, making yourself one with the darkness.  As long as you remain within 10 feet of some kind of shadow (except your own shadow) or within at least moderate darkness, your ability to hide is greatly enhanced.  You can hide yourself from view in the open without anything to hide behind, even while being observed, and you gain a +20 circumstance bonus on Hide checks. 
  Unlike invisibility, this spell’s effects do not end when you attack, though you cannot hide and attack at the same time.  You are clearly visible while attacking (and thus do not gain a +2 bonus on your attack for being invisible, nor is your target denied its Dexterity bonus to AC), but you can use a move equivalent action to hide again after attacking (or hide as part of a move action), and you still gain the +20 circumstance bonus on your Hide check.  Your opponent can ready an action to attack you when you come into view to attack. 
   

Here are possible alternatives:

invisibility
the Hide from Undead spell
the Silent Image spell, via opaque image to break line of sight (LoS), such as fake wall
the Wall of Gloom spell (Complete Arcane, p.129), see Silent Image
sort of the Ring of the darkhidden wondrous item (Magic Item Compendium, p. 122 (or Magic of Faerûn, p.146))
the Shadow template (Lords of Madness, p.167)

Shadow Blend (Su): In any conditions other than full daylight, a shadow  creature  can  disappear into the shadows, giving it total concealment.  Artificial illumination, even a light or continual flame spell, does not negate this ability, but a daylight spell will.