In the world of Harry Potter, Hogwarts subjects are hard enough without adding Potions Classes into the mix (and that too under the inequitable guidance of Severus Snape.) Still, as he himself states, this art form can help students "how to bottle fame, brew glory, and even put a stopper in death."
This obviously does not mean that all potions have value — although several are quite practical, indeed — because there exist concoctions that are so strange and pointless that it is a wonder why they are even part of the school's syllabus. The list below includes a few effective potions along with an equal number that have no place in academia.
Best: Elixir To Induce Euphoria
A sixth year potion, the Elixir to Induce Euphoria is chosen by Harry during Professor Slughorn's class in an attempt to tempt the latter into revealing the actual story behind young Tom Riddle's questions about Horcruxes. It's hue, a warm yellow, indicates an association with bright, sunny days, and is said to create an extremely elevated sense of joy if consumed.
The side-effects of the Elixir to Induce Euphoria apparently includes a predilection towards bursting into song at the most inopportune moments, but they are certainly worth it if the potion does what it claims.
Useless: Draught Of Living Death
The Draught of Living Death is far too dangerous to be so casually taught in Hogwarts Potions classes: imagine if some idiot pupil pours a few drops into his mouth, or worse, pranks his friends into doing it. The potion can force anyone who drinks it into an endless slumber, quite like those many fairy tale princesses are cursed into.
More importantly, preparing the Draught of Living Death is particularly complicated, as even Hermione was fully unable to master it in the short duration given to her. What are these curriculum developers even thinking?
Best: Strengthening Solution
The Strengthening Solution is not only great because it supplies its drinker with overwhelming amounts of physical strength, but also because the Ministry of Magic (through Dolores Umbridge) is terrified that students might incorporate it into their "arsenal" if/when a "coup" is planned. Typical politicos.
They aren't entirely wrong to be so paranoid, though, as greater strength could be useful in battle, especially if one gets disarmed midway (one could just crush a boulder with their bare hands to intimidate their opponent.)
Useless: Invigoration Draught
It isn't fully clear what an Invigoration Draught actually does, but it seems that it restores, maintains or enhances the user's levels of energy. This might seem an efficient way to spend school sessions, but how different is it from, say, a bottle of Gatorade?
Of course, the Wizarding World would not purchase Muggle products, but it makes no sense that they wouldn't have a spell that does the same thing except much quicker. For instance, the counterspell to Stupefy, Rennervate, literally means "to furnish with energy."
Best: Sleeping Draught
Interestingly, the Sleeping Draught is considered a rather easy potion to create, but unlike its cousin mentioned above, the drowsiness and duration of sleep involved is far shorter. Think of it like a hefty dose of Muggle melatonin (a hormone-based substance that is used to combat insomnia.)
The effects of this potion are quite powerful, nevertheless, as it allegedly works on the dragons imported from Romania for the Triwizard Tournament. The key thing to remember here is that the Sleeping Draught is easily reversible; the only requirement is time.
Useless: Wit-Sharpening Potion
It is extremely bizarre that a potion that assists in cognitive improvement, working memory functionality and overall alertness is actually allowed to be in the textbook, because the capacity for it being misused (cramming for tests) is quite diverse.
This doesn't mean that the Wit-Sharpening Potion is wholly worthless, but it just feels like the drinker would be gaining a massively unfair intellectual advantage. That being said, maybe Harry should have taken a swig of this brew before running off to the Ministry in order to "save" his godfather.
Best: Draught Of Peace
This potion seems to have limitless potential in applicability and significance, as seen by the fact that Madam Pomfrey regularly doses frazzled fifteen-year-olds with the Draught of Peace so as to help calm their stress about the upcoming O.W.L. exams.
The only problem is that it's one of those elaborate recipes that require multiple ingredients, carefully choreographed mixing procedures, and confusing temperature changes. Also, going even slightly wrong could result in it backfiring severely — either via explosion or by inducing a comatose state.
Useless: Shrinking Solution
The Shrinking Solution is discussed in the third year, with Professor Snape assigning his students this concoction in the first class itself. In the story, it is claimed that this potion is supposed to reduce the size of anyone (or anything) who drinks it, but when tested on Neville's poor pet, Trevor, it reverts into its larval, or tadpole, stage.
This clearly implies that there are aging factors at work here, because the result of this cruel experiment should have just been a tinier toad. Imagine becoming a baby by mistake!
Best: Love Potion
Depending on the intensity of outcome desired, Love Potions can be either simple or horribly complicated. The standard version isn't permanent, unlike Amortentia, which can be identified through the nose (a unique assortment of fragrances based on what the "smellers" adore the most.)
However, even low level ones made by the Weasley twins are potent enough to influence Ron, as he becomes unbearably infatuated with Romilda Vane almost instantly. Would it work on Lord Voldemort as well as it worked on his father, though?
Useless: Felix Felicis
Felix Felicis is an incredible potion, but only in theory. The so-called "Liquid Luck", a gold-burnished mixture (transparent in the films), seems to extract convenience and good fortune from invisible pools of magic and delivers it to the drinker.
Harry has had great success with Felix, but Slughorn warns him that it can be quite harmful if precautions are not taken. Forget that it takes six months of exhausting work; if this potion is drunk in excess, the consequences — becoming dizzy, careless and overly courageous — are far too dire to balance out the luck obtained.