Imperial Worlds
Designated by function
Agri-Worlds
Agri-Worlds are planets in the Imperium of Man entirely dedicated to agriculture. A typical agri-world is mostly covered by millions of square kilometers of farmland managed by a few million farmers and a couple of spaceport cities/transportation hubs where stuff is loaded onto starships to be sent elsewhere to feed the Imperium's teeming masses. Said ships also drop off huge loads of shit (sometimes literally) to keep things fertile. Others are Ocean Worlds with huge fish farms or Gas Giants with habitable zones and balloon bases that collect airborne plankton and mash them into Soylens Viridens. Their tithes are paid in whatever edible products they grow, which, combined with their relatively sparse population, means that they rarely have to raise regiments for the Imperial Guard. Some still do, of course, as need allows or a small number kept in the Sector and well supplied. Other Agri-Worlds are defended by Imperial Knight Houses, becoming Knight Worlds. The Administratum has a somewhat dickish tradition - of course - of promoting them all as rural, bucolic paradises regardless of what they are actually like (although worlds like that certainly do exist in the Imperium, it's more likely that they would be pleasure worlds, garden worlds, or simply a barbaric world that hasn't been colonised yet).
Cemetery Worlds
Extremely depressing worlds that are dedicated almost entirely to being huge graveyards. Cemetery Worlds see some religious overlap with Shrine Worlds, and are considered sacred and solemn places by the Imperium at large and especially the Ecclesiarchy. Most if not all of these worlds are not simply covered in row after row of grave plots, though one might assume some Cemetary Worlds are surfaced in nothing but geometrically perfect grave tessellations, broken only by small hills with singular willows to be sad under. Some have cathedrals clad entirely in human remains, or catacombs that reach many kilometers into the planet's crust. Certain Cemetery Worlds are dedicated only to the deceased of certain organizations or sub-sectors, though these are very rare.
These should not be confused with Mausoleum Worlds, which are a sub category of either shrine worlds or, more usually, Space Marine worlds.
Forge Worlds
The Imperium's massive workshops. Forge Worlds are planets dedicated entirely to industry, are technically a sovereign world of the Mechanicum, and the property of the Adeptus Mechanicus.
Hive Worlds
Exists for cramming tens of BILLIONS of people into on planet, obviously. Grimdark for underhivers.
Shrine Worlds
Shrine Worlds are worlds completely dominated by the Ecclesiarchy. They are famously paved in cathedrals, monastaries, reliquaries and catacombs. While never truly reaching Hive World status, many of these worlds are nonetheless stuffed to the gills with pilgrims, caretakers, priests, and the officers of the Imperial Cult. They make excellent homeworlds for Orders of the Sisters of Battle. Any Guard Regiments raised will be fanatical in their service. Frequently hosts Scholae Progenia as well.
SPESS MAHREEN Worlds
These are planets claimed by a Space Marine chapter. While typically most Chapters select Death Worlds, Feral Worlds, or Feudal Worlds as a home due to the hardiness of their residents, some of these planets are more civilized or even at a better standard of living than most of the Imperium - the Realm of Ultramar is an obvious example of the latter.
Tithe Astartes planets are notable for being one of only two planet types exempt from the usual Imperial Tithe, with the only other type being Aptus Non (read: planets which have been Exterminatus'd). This does lead to a few political complications. For instance, Space Marines can technically claim a Hive World for recruiting, and some do, but because the tithe of the world is then denied for the recruiting of guardsmen it creates tension between the chapter and the Adeptus Munitorium.
Designation by development level
Feral Worlds
Feral Worlds are places where mankind has regressed to the level of the Stone Age. While they're as primitive as it gets, they are prized for the high quality of their warriors. There are numerous kinds of Feral Worlds, from stereotypical "Neanderthal worlds" (like the ones which spawned the Ogryns) where humans are brutish hunter gatherers wearing pelts to Techno-Barbarian worlds where everything has gone Mad Max or Waterworld. Some Feral Worlds are closer to the Neolithic Age, and have recognizable urban civilization and culture. There isn't a lot of official nomenclature for the numerous sub-variants of these worlds. Imperial Tithes from Feral Worlds tend to be either nonexistent, or in manpower for the Imperial Guard. Occasionally these worlds will have some natural resource which the Imperium decides it needs, so they can be colonized by more civilized Imperium citizens or Mechanicum Servitors, who set up isolated bases of operation amidst the "barbarism". Favored for Astartes recruitment due to probably hellish life conditions.
Feudal Worlds
Feudal Worlds are planets abandoned by the greater human species during the Age of Strife and for one reason or another regressed back to pre-engine (steam or otherwise) technologies. They are also generally divided into small kingdoms which fight with each other but pay tribute to the Imperium. Because apparently the Neo-Medieval themes of 40k just weren't enough so they had to add in several actual medieval-themed worlds too. The Imperium deliberately keeps them from progressing further technologically with only a small handful of exceptions, since the Imperium already works on a form of the feudal system anyway. More importantly, it ensures that the planet's citizens know their place in Imperial society and don't get any ideas about secession into their heads. But the big reason why these planets are kept around is because they provide good light infantry for the Imperial Guard and Space Marines like to recruit from there.
Knight Worlds
The Knight World is a special variant of planet, somewhere between an Agri-World and a Feudal World. These worlds are only found in planetary systems with Forge Worlds (or at least close enough that a short Warp jump is enough to bridge the gap), and are more within the legal vestibule of the Mechanicum, not the Imperium. Since Forge Worlds rarely harbor any kind of agriculture, Knight Worlds supply Forge Worlds with the huge amount of food it needs to survive, and sometimes help fulfill their mineral quotas as well. In turn, the Forge World supplies the kingdoms of the Knight World with Knight Titans, huge war machines with which the kingdoms may defend themselves from rampaging mega-fauna, Chaos incursions, Xeno invaders, and the Knights of other kingdoms. When the Forge World is in need of defense, or when a local Exploritor is going on a quest, the Knights and their well-trained pilots (and squires, attendants, and etc.) are called upon in whole or in part to "ascend to the stars and fight amongst the gods."
Civilized Worlds
Civilized Worlds are the 'normal' inhabited planets in the Imperium. Lacking Hives (or at least having one or two per continent at most) or Forge-World-scale factories they never the less have a decent level of technology and a population in the same ballpark as modern Earth (5-11 billion souls). Due to lack of fluff, this may be the most common type of planet in the Imperium, but seriously, are you in the game for a chance to edit wikis in the 41st millenium? Many of Ciaphas Cain's novels occur during campaigns to defend civilized worlds, this actually helped to tone down a great deal of the Grimderp of 40k early editions, by actually giving the imperial armies populations and places to defend which you could feel emphatic with because you know, it's good to know even at the beginning of the 42nd millenium there are still snack vendors, cafeterias and pubs.
Pleasure Worlds
Pleasure Worlds are a subtype of civilized worlds, sporting exquiste wine estates, views Hive Worlders will never even see a picture of, and much more. Essentially tourist traps and vacation spots IN SPEEEHS, which are predictably restricted to the exclusive use of nobles, senior officials of the Adeptus Terra, and other big shots in the Imperium. These worlds are often hotzones for Slaaneshi cultists, because why not turn some of the Imperium's most powerful men and women to Chaos when they're on vacation? As of 8th edition, even Pleasure Worlds are supporting war by setting up hospitals, providing rare medication and other whatnot.
Designation by status
Paradise Worlds
Different from Pleasure Worlds, Paradise Worlds are merely a joy to live on. Either lushly verdant or impressively architectural (or both!), Paradise Worlds are as far from the Imperial front lines as one can reasonably get. As war can and will find its way to Paradise Worlds, no well-known examples have remained in this world classification for very long. Many of the remaining Paradise Worlds are self-sufficient, with farming and housing and industry all balanced perfectly. Many of them are relics, with histories that span back into the Dark Age of Technology (somehow without civilization-ending calamities). Paradise Worlds are jealously guarded and staunchly defended both politically and militarily. Some Knight Worlds are Paradise Worlds, such as Voltoris, home of House Terryn.
Dead Worlds
Exterminatus isn't the only way planets die. Ecological disaster, sudden celestial events, alien invasion, someone disengaged from the warp too close to the planet and accidentally the atmosphere... Keep in mind, unlike the entry below, these aren't strictly forbidden for colonization, its just the work required to make it habitable is prohibitively expensive for the negligible gain in resources. Most would require either completely isolated arcologies, underground cities, or huge terraforming projects. Tyranids create these worlds en masse: after they nom all the life on the planet, they will then turn to draining the planet of its core, atmosphere, and any water still remaining before setting off for new real estate.
Barren Worlds
A sub-classification of Dead World; a Barren World is the Dead World's less awful little brother. It is a world which has never harbored life, nor could it without substantial terraforming. Mars in M40 (and M2) is a good example of a Barren World, or it would be if it wasn't already a Forge World (and a Hive World in it's own right). These worlds are often colonized for mining.
Death Worlds
Death Worlds are worlds where everything is hostile to Human Life (think Australian outback on crack). And that means everything. The animals, the plants, sometimes even the very air itself is fatal for humans, while being just habitable enough to warrant colonization. Examples include Catachan and the majority of Astartes homeworlds.
Quarantine/Forbidden Worlds
While it seems cut and dry what kind of planet this is, these tend to have a large spectrum of why they are blocked off and how it is enforced. For the most part, the reason is heresy: the planet has fallen to Xenos influence, worships Chaos, or broke off from the Imperium. Others include mysterious perceived danger. A planet being a Death World is one thing, but if the last five colonization attempts on a planet ended with the inhabitants mysteriously vanishing, the Imperium is going to block it for settling and generally tell the Inquisition to figure out what is going on. The Inquisition rarely does, and so Forbidden World they remain until everyone forgot why they were forbidden, and they send another settling party down...
War Worlds
War Worlds are planets locked in eternal war. So what makes these planets different from just any old planet with a war on it? Scale and length. Generations of soldiers have lived and died. Some planets, as well, just have such warlike cultures that even without an external force, they will kill each other (not necessarily for Khorne, usually planets with scarce resources ——such as Zayth, but that's a Hive world—— result in this, since the best way to deal with limited supplies is to kill someone else and take their stuff). Some of these worlds just happen to be unluckily situated in a location so strategic that two intergalactic factions refuse to acknowledge the sunk-cost fallacy and back down.
Many Imperial groups maintain War Worlds as a means of keeping battle-trained troops at the ready. They are useful for Guard and Space Marine recruiting and act as a natural deterrent to planetary conquest or invasion in important areas.
For the most part, these are probably pretty shitty places to grow up in, even by Imperial standards.
/tg/ worlds
Imperial Daemon Worlds
See Terranis in Love and Krieg Spinoffs.