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You will therefore find in quite a lot of Speculative Fiction, the notion that energy is just another form of matter -- particularly, a sort of warm glowy kind of matter, whose exact properties can be fine tuned to user specifications, and which can be summoned or banished with a button-press.
In this sort of system, you can treat "Pure Energy" as a building material, and make things out of it. Such things would, quite naturally, be of higher quality than anything made out of mundane old matter. In the universe of real physics, claiming something is "made out of pure energy" is flat out nonsensical -- it makes as much sense to say that something is "made out of pure velocity," or that pasta is "made out of yummy". (It is, though.)
If we're feeling generous, we can suppose that they don't really mean to treat energy like a kind of matter, and are actually dealing with highly energized exotic matter, such as plasma, certain created energy sources or Phlogisticated Aether, but they really shouldn't be going around calling it "Pure Energy".
In Elemental Rock-Paper-Scissors settings, this enables "energy elements" -- Fire, Lightning, Light, and Darkness -- to be treated and manipulated the same as "material elements" -- Air, Water, Earth, Metal, Wood.
Misinterpreting the law of conservation of energy - "energy cannot be created or destroyed" - to mean that objects made of "Pure Energy" are indestructible is a common subtrope. Of course, if "energy cannot be created", then we're left to wonder how, according to this subtrope, "Pure Energy" came into being in the first place. Or why the same rule doesn't apply to stuff made of Pure Matter (as the actual LoC does). 
- Energy Ball: An orb of the stuff usually used offensively.
- Energy Beings are people made of Pure Energy.
- A Swirly Energy Thingy is a Pure Energy-based Cool Gate.
- Laser Blades are swords forged out of the stuff.
- Sword Beams are beams that shoot out from swords.
- Deflector Shields are usually walls made of Pure Energy.
- Hard Light, when it's just "we turned up the power so high that it became solid" as in Automan, is a solid projection made of Pure Energy.
- Frickin' Laser Beams are, by and large, simply conventional pistols that fire bullets made of Pure Energy, rather than being lasers or something similarly hard to dodge.
- Objects made by a Green Lantern Power Ring.
- Power Source to most advanced or magical machinery.
- Frequently a source of Non-Elemental damage.
- One of the brands of Leggs® panty hose was called "Sheer Energy".
- Smax in comic Top 10 can fire energy from his chest. This is later named "The Strong Light."
- The "Pure Energy items are indestructible" thing shows up all the time in the Marvel Universe.
- Cyclops releases blasts of "pure concussive force" from his eyes.
- In the WITCH comic Will's element is defined as "Pure Energy" while the rest of the Guardians are a Four-Element Ensemble. In the TV series her element is defined as "Quintessence" which is basically Shock and Awe mixed with Lightning Can Do Anything.
- One episode of Blakes Seven features a force wall whose optical properties had been set such that it was indistinguishable from a normal door.
- Star Trek, the original series at least, might as well be the trope namer. The number of times Spock says "Pure Energy" over the course of the series is only rivaled by the number of times he says "Near Earth parallel, captain."
- In third edition of Dungeons and Dragons, non-physical damage types like fire, electricity, and acid, are referred to as "energy damage," in a nod to logic and reason. And they all end up being used in practically the same manner as Pure Energy anyways.
- Meanwhile, in third edition at least, magic missile spells are made of force, which is basically the same thing as 'pure energy'. Other force effects include the Bigby's line of spells, and a dragon that BREATHES force energy.
- Warp Energy in Warhammer and Warhammer 40000. Technically it's psychic energy, composed of the thoughts and emotions of every sapient being, but in practice it is treated as this trope.
- Mega Man Star Force 2 featured Matter Waves. The futuristic society in the series essentially does just about everything using energy waves, such as creating snow for a ski resort, making fountains, and controlling... the... weather. Ignoring all of the completely ridiculous things done with it, however, you still have the Matter Waves, which are basically electromagnetic waves in tangible form. You have Matter Wave Skis, Matter Wave Vacuum Cleaners, Matter Wave MacGuffins, and Matter Wave BUTLERS.
- Lost Planet has "Thermal Energy", which is harvested by killing Akrid. It's some kind of glowing orange goo that has a large potentency. Possibly overlaps with Green Rocks.
- Half Life's Combine Dark Energy Orbs are balls of energy either kept in a stasis and used to power generators, or contained in a capsule which can be used as a weapon, releasing the orb which instantly disintegrates most biological lifeforms it comes in contact with.
- Final Fantasy VI has the boss Atma/Ultima Weapon, which before the battle boasts of being "pure energy, and ancient as the cosmos." It is no pushover.
- Which is why beating it by draining all of its MP makes sense - without MP, it's as good as non-existent.
- In Might and Magic VI, gold dragons and energy drakes hand out "energy" damage as distinct from fire, cold or electric, and so do "Ancient Weapons".
- Gene Catlow has seen a lot of this after Friendship Island was introduced.
- Just. Pure. Energy.
- This is a pretty common power type in the ‘’Global Guardians PBEM Universe’’. Victory, Evengella, Argent, both Quantums (one an American superhero with vast and near-limitless power, the other a Spanish hero with not quite as much power), Silverwing, and the Chaos Lord all use the “cosmic energy” rational, and some use the “energy can’t be destroyed” assumption as well.
- In the 2009 Astro Boy movie, the title character is powered by a glowy energy that is "more powerful than nuclear energy." News flash, folks: Energy is energy. You can say you have more watts or transmit at a higher voltage, but energy does not come in "flavors" that are better or worse than any other.
- In Transformers, Energon, so near as we can tell, is Pure Energy which has been poured into a box for easy storage.
- The late G1 episode, "Call of the Primitives", featured a monster named Tornedron who was described as being made of "pure energy", thereby allowing him to assume many (apparently solid) forms and making him superior to Unicron, a being of matter... riiiight.
- Other incarnations, like Beast Wars, made Energon into a form of Green Rocks that generate a lot of power and have all sorts of funky effects.
- G1 Energon is weird. Any source of fuel can be poured into a cube made of... white outlines... and once inside, it promptly turns into glowy stuff that robots can drink or use to fuel stuff. All the other series (including Beast Wars, which actually follows G1) treat it as a natural resource that can be mined. It still blows up if you rub it the wrong way, though. Interestingly, most if not all weapons made of Pure Energy in Transformers are called "energon weapons". They seem to be quite solid. In Transformers Animated, the shiny parts of a weapon that's mostly made of shiny can hold the solid parts in place. It's... pretty safe to say that it all runs on Rule of Cool.
- In the movie Titan A.E., an entire race called the Drej and all of their ships and weapons are made of pure energy. The mind boggles.
- Of course, that stops bothering you once you see them use the Drej as a giant Battery.
- Dexter of Dexter's Laboratory once tried to produce pure energy in his laboratory. In the few moments before his machine crashed, it was depicted as a giant glowing atom (you get a better view of it in his grandfather's Rube Goldberg machine).
- Megabyte in Re Boot once extracted all the energy in Mainframe's core and converted it into a liquid state which was stored in a "transformer". But since this pure energy was unnatural it caused problems when the User loaded a game, including forcing the game to land on the Principal office, corrupting the game and turning Megabyte into a Megatruck.
- The actual formal definition of energy isn't so confusingly circular, but takes a lot more time and effort to explain
- One source of confusion here is that in laws of conservation, "destroy" means, more or less, eliminate entirely from reality. In everyday usage, though, it simply means "dismantle into lots of tiny bits" — even if you think you eliminated the thing from reality. When you "destroy" a piece of paper by setting it on fire, you're not violating physics, because that's a different sense of "destroy". The paper no longer exists as "paper", but as lots of molecules once connected as "paper". In the sense of the LoC, fictional characters indeed have no hope of "destroying" a Pure Energy object, but they don't have any hope of destroying a basketball either — only of (in either case) breaking it down into lots of tiny bits.