As a breeder I've spent a lot of time breeding IVs for these different hidden powers (which is quite a task), and feel a certain connection with them. In any case, I think I have some things to say about them.
The ones I (and others) breed the most are as follows (not in any order):
-Ice
-Fire
-Electric
-Grass
-Fighting
-Ground
As some have said, many of these are bred for coverage, and to hit specific pokemon. Here's my opinions (more like observations) on them:
Hidden Power Ice:
Number 1 bred for hidden power, and for good reason. Outside of hitting the dragons and gliscor for 4x super effective, it has amazing coverage with a variety of other attacking types. Electric/Ice, Ground/Ice, Fighting/Ice, and others. The pokemon we breed it onto are:
Electric Types: Are notorious for generally having terrible coverage, especially since none of them outside of lanturn learn ice beam. Ice is the best type coverage for their stab, and most of them are special attackers, so as a result HP ice is highly desirable on almost any electric type.
Grass Types: Grass is walled by some notable types, including dragon, flying and other grass pokemon. While Ice doesn't provide perfect
coverage (walled by fire) it goes a long way. None of them outside of ludicolo learn ice beam.
Fire Types: Fire, like grass, does not gain perfect coverage with hp ice, but ice helps against the dragon types who would resist you. In general, fire types can make use of a lot of different hidden power due to lack of synergy in coverage with other types, but ice is a stand out on many notable ones:
Infernape: Gets grass knot and thunder punch, making grass and electric HP less desirable. STAB fighting makes hp ground for heatran not-so-attractive.
Heatran: Gets Earth Power. Electric and Grass are also sought after, but overall ice is most valuable for having great coverage with Earth Power.
Other pokemon like Lucario and Togekiss like Ice just because it hits very notable threats. Gengar, and even dugtrio can use it to pick up valuable revenge kills on the 4x weaks. There has been some discussion of even running HP ice on heracross, though overall not a great plan. In conclusion though, ice is an amazing attacking type, and HP ice is desired for good reason.
Hidden Power Fire
Hits steel types, notably scizor foretress for 4x effective. Considering steel's amazing resistances, and fire being the only consistant weakness on most of the OU steel types (metagross, skarmory, bronzong, scizor, forry), fire is desirable on pokemon who would be walled by them. The saying, "Anything physical wants a little bit of fire."
Grass Types, again, suffer from having a great attacking type with crappy synergy with other types. Fire is the most popular option next to ice because of its ability to hit bugs, steels and other grass types, all of whom would wall you normally. On a side, many grass types like being in the sun, making hp fire even more attractive for getting its boost.
Dragon types generally have access to flamethrower and fireblast, but Latias and Latios have some desire for hidden power fire.
Most physical attackers like tyranitar and machamp already have access to fire attacks though, so the above metioned grass types are the most common users.
Hidden Power Electric
hits Gyarados, and other bulky water types (except swampert). There are very few special attacking ice types that don't get thunderbolt and see a lot of play (because let's face it, ice is a crappy defensive type). In the end, electic is for pokes who really need to hit water types. Generally these are:
Water types themselves. Kingdra, Vaporeon, Milotic, etc. are the pokemon most sought with hidden power electric. In a mirror battle between water types, carrying a good hidden power can be important, especially when most water types can't get grass or electric attacks, and those that can usually abuse them *starmie*cough*
Fire Types can sometimes make use of it, but many of them already learn electric attacks on their own. Otherwise, electric provides pretty unsatisfactory coverage with fire.
Hidden Power Grass
Like Electric, it's popular with water types to hit other water types. Swampert and Gyarados existing together in the same metagame is really annoying, but their dual presence creates a need for a type of guessing game about which power to go with.
Electric types, also like HP grass almost as much as ice, if only because it can be a nasty surprise for swampert.
Some rock/ground types like Tyranitar and Nidoking might want to stow away some IVs for Hidden Power Grass.
In UU, grass is generally more useful than electric, though mantine's dual presence alongside gastrodon and friends creates a similar situation in UU regarding water types.
Fighting
Hits Dark types hard. Can also provide great coverage with other common attacking types like ghost, dark and ice. As a result, these are the types of pokemon who use hp fighting the most.
Psychic types-- who don't get focus blast, and even ones that do, like HP fighting for coverage.
Ghost types-- pretty much same story as psychic types. For both, being able to somehow handle weavile and ttar is a huge boon.
dark types-- not incredibly common, but can be useful on some, notably houndoom.
Bug Types-- oddly, things like venomoth can use it really well.
Ice Types-- Some of them, like Glaceon, like this.
As a weird aside, Rotom can make good use ice or fighting-- it can use the bolt-beam or ghost-fighting combos to good effect.
Hidden Power Ground
Hits heatran for 4x, and empoleon for 2x. This is something important to note for Specsmence.
Electric types also like to sometimes run HP ground to get a jump on their fellow ground types. It's kind of a gimmick over coverage, but it can work really well sometimes.
Bugs, such as venomoth, butterfree and Yanmega can also use them to achieve some very nice coverage.
Grass types can again, use this to take care of fire types (read: heatran), but grass/ground has TERRIBLE coverage (poor torterra).
Special attacking ice types like Lapras, Jinx, Glaceon, like this.
Interesting aside, Frosslas, with the aid of HP, can use any of the following: bolt beam, ice-ground, ghost-fight, ice-fight, basically getting amazing coverage with any 2, but can even run 3. Yeah, frosslas is cool.
The others, don't come in much demand.
A word to the OP: The only pokemon HP bug hits for 4x is Celebi, and considering Celebi's plethora of common exploitable weaknesses, hp bug is not coming in much use. Grass has 5 weaknesses. As for psychic and dark types, dark, ghost and fighting attacks are everywhere. HP bug has very little going for it in reality, and lacks synergy with more common attacking types.
