In a basic sense, puzzles in adventure games are very simple: you have discrete objects, with different stats. By combining the right objects, or perhaps taking the right action type, you can advance through a chain of causality; eventually unlocking the final "win" state of the game.
I find it useful to see this bare abstraction that lies underneath everything; but obviously it's also so abstract that it's hardly helpful when really sitting down to craft puzzles. So let's describe them some more.
Control of Objects
One way to categorize puzzles is by thinking of the different kinds of objects involved, which are themselves categorized by what kind of control you have over them. There are usually a minimum of two cateogires: inventory, and environment objects. Let us also strip these down to their essentials.
Types of Object
An inventory item is movable, and so can potentially interact with many other objects in the game (lots of possibilities = harder), and often can be used more than once. Inventory items can usually also be combined with one another, possibly to form new objects.
Objects in the environment are stationary, and so can only interact with inventory, or sometimes objects in the same location (fewer possibilities = easier). They tend to completely change form less often. And it's rarer for them to interact with object in different location (e.g., a valve in one spot that causes water to flow in a different location, with pipes seen in both).
A third, intermediate, type exists: items that have not yet joined your inventory. These are special because usually the interaction with them is extremely limited; you don't solve puzzles with them, but simply pick them up. They are often rewards for solving other puzzles.
A fourth intermediate category is also used in some games: internal notes, memories, or data (or perhaps spells). These function sort of like inventory, sort of like action commands, depending on execution. Often they can be combined heavily with each other, but not with other inventory. They can be used on NPCs, or change dialog options with NPCs, but do not engage with more physical or mechanical puzzles. For example, some of the Blackwell mysteries from Wadjet eye used a notebook of clues; as did some Sherlock Holmes adventures from the 90s. (Loom had its spells, but you might look at these more like regular action commands.)
The Puzzles Based on Object Types
I don't need to be pedantic here: you can see puzzles being based on each of these types in isolation, or in combination with two or more of them.
Puzzles entirely based on the environment may be rated easier, on the whole, but this depends on the number of actions a game has: if there are only two -- "look" and "act" usually -- they become quite easy, while a SCUMM system with many verbs is harder, and open-ended text-parser commands may be just as hard as inventory-puzzles.
Now let us look at things from a different angle, and concern ourselves with some standard types of puzzle, as they familiarly appear.
The Puzzler's Puzzle
One unique category is the true puzzler's-puzzle. These appear as mini-games played on a sigle screen, with numerous sub-components that do not leave it or ever join inventory. Many interactions are possible, making trial and error usually too onerous. Solid deduction is necessary, maybe with pen and paper as aides. They oftne involve mathematics, word-games, cryptography, or rearrangement of tiles and such. In some very puzzle-centric adventure games (which one might not even give the name), these dominate, and a little travel exists mostly to get from one to the next. In more diverse adventure games, they may appear occasionally; usually they are not very integreated into the environment, or other puzzles -- except perhaps that they begin with missing components, and cannot be started until those are acquired..
All other puzzles are in some sense "environmental" then, since they deal not with pure abstraction, but with the surroundings, tools, and characters in the setting; are at least thinly tied to a plot; and usually more integrated with one another. But there are many kinds of these.
In this puzzle, you are also largely interacting with objects in the environment, setting them to some desired state and -- very importantly -- figuring out what they all mean and do. This is practically very similar to the last type but with two distinctions. First, it is physically distributed across multiples scenes, with many parts that interact. Second, there is some guise for the abstract puzzle inside it. Often the player finds himself inside some kind of device or factory, and interacts with different computer terminals or other components. Many of Myst's puzzles were of this category; just a step removed from a pure abstract puzzle.
This is similar to the above type, in that you come across something with no known purpose: and it's your job to figure it out before you can even apply it to some other challenge. The difference is that here we have a single, small object, possibly in your inventory. The puzzle involves this box's many inputs and outputs, which give clues on use. This kind of puzzle thrived in the text adventure days: every object needed investigating, and it was easy to program copious feedback on the many false-attempts the player would inevitably make -- and that is key: generic "that didn't work" feedback makes it impossible.
Among the more boring type of "puzzle," but nonetheless used as filler in a great many games: an NPC or device requests something, and you must deliver it to get the reward. In some cases, the exact object is unknown, but its desired properties are given -- as in a fairy tale riddle.
Here the player must jury-rig some expedient technical device, using ordinary objects. The results are often far-fetched, but if the expectations are set up for this kind of solution, they can be quite enjoyable. Success usually hinges on making some logical leap about objects' properties and possible uses; and often on a grasp of physics or mechanics, to see what might be required. Multiple objects are needed, often from inventory.
Many games thrived on this kind of puzzle. But the downfall is drifting away from controlled, physical circumstances as a mileau: characters and animals, for instance, don't behave predictably and precisely; puzzles that pretend they do become illogical and frustrating.
Key in Lock
This is something of a catch-all, but adequately describes many smaller puzzles, where the player makes an incremental advance by obtaining one new useful item, making a new location available, and so on. It is a close cousin of the MacGuyver-type puzzle, but much smaller, and not necessarily so mechanical; rather than build elaborate devices, usually just one item from inventory is needed in an unusual spot. So it is a key and lock, but not an obvious lock.
These are the work-a-day kind of puzzle for most adventure games. The difficulty can range widely, depending on the availably permutations of objects, and how big of a leap is needed to determine why the key will fit.
Hunt the Pixel
Infamous for being annoying, the player is here required to spot a small object to pick up or interact with. Myst had a small red button on the floor, for instance. Many inventory objects are made more "difficult" to acquire with this method. It is best avoided, unless good clues are given that something is available.
Here, the final "puzzle" may actually be very trivial -- using the right object in right keyhole, again -- but there is no logical connection to be made. A connected set of clues must be pieced together, which will reveal the correct choice. "Which door is the right one?" might be answered this way. The clues themselves can be very simple or quite complex, involving various pure-puzzle elements like cryptography to unlock, or to combine -- i.e. one set of puzzles provides the floor of the parking deck you need to be one, another the colored zone. NPCs are often dispensers of some of these puzzles. Interestingly, this is a case where pure information is the key; no new inventory objects are needed to get the solution -- perhaps no inventory at all.
The set-up for these often depends on a large number of choices, which has to be narrowed in some way. It can work for mazes, for instance, and learning the one correct path through. In practice, games may handle trial-and-error attempts in two ways. By allowing their success, the world is made consistent: the correct option always existed, and the player may abandon clue-hunting to make and educated guess at any time. By barring their success -- e.g. the correct door cannot even be selected until all clues are found -- the importance of the protagonist's knowledge is created: he or she will not attempt crazy thngs without reason. Both have their advantages, but the latter seem more popular in recent memory.
When designing a game, one might consider up front the sort of puzzles it will include. It's hard to make a case against variety, but I don't think there's a huge advantage to hitting every single option, just for the sake of it. Some kind of theme can help make puzzles work mesh up, or at least feel like they belong in the same story. One inevitable decision is whether isolated "puzzler-puzzles" have a place in your game. Then, whether the more elaborate MacGuyver ones do. The genre of your world, and the particular story, might also guide the way. I think there is also a philosophical choice right up front: does the "adventure" exist to serve the puzzles, or the other way around?