Alternate Universe: You can freely travel between the human world and the Denjuu world via "antenna trees" that give out a special electrical signal, but only if your cellphone has really good reception.
Arm Cannon: Many, many Denjuu gain these upon evolution. While it's somewhat understandable that a monster fused with an inorganic item would grow missile launchers that way, a few of them seem to have started out like that on their own.
Awesome, but Impractical: Special attacks, at least in the first game. Penguin Missiles and Mega Flames sound great, but they take several turns to charge and often miss their target anyway. The sequel fixed this in a major way, with the charge time replaced by a Denma Points bar and even more awesome attacks such as sharing giant healing strawberries with party members, cutting up an opponent with a wireframe, and sending an opponent off of a rocket to Mars for an instant win.
Bag of Holding: The player is able to carry up to 99 of every item. This includes bazookas, personal computers, solar panels, blenders, oxygen tanks, and so much more.
Batter Up: In the manga adaption of the first game, Shigeki uses his aluminum bat extensively to assault various Denjuu, although it is often damaged or destroyed in the attempt by their superior claws and teeth. One notable incident has him goading his hot-headed partner into attacking him at high speed so that he can whack him with the bat into an enemy Denjuu, just because it seemed like it would be a cool thing to do.
Bonus Boss: In the first game, there is a locked room very early on which only becomes unlocked after you've beaten the main storyline. There you can choose to fight one of a pair of sisters, both of which have a team of three maximum-level Denjuu.
Combat Tentacles: Cute, pink Punica has a single tentacle on its head, but grows more as it evolves. Its ultimate evolution is Veenica, which can shoot harpoons out of the ends of its many paralyzing, stinging tentacles.
Cool Horse: Berzelia is a rather decent, if bizarre-looking, giant-hooved horse/zebra Denjuu available in the first game. If centaurs count, then Ornithogalum definitely fits here too, being a Denjuu so secret that he wasn't included in the players guide, could be obtained any time at level 50, and was one of the few Denjuu who appeared in both games. Also, he's on fire.
Corrupt Corporate Executive: In the first game, the leader of Sanaeba pharmaceutical company (who discovered the Denjuu world) attempts to manipulate the Denjuu for his own gain with assistance from the Big Bad.
Defeat Means Friendship: Beating the snot out of Denjuu is the only way to impress them enough so that they'll give you their phone number, so that they may assist you in beating the snot out of more Denjuu.
Die, Chair! Die!: Vases can be picked up and thrown. This is mostly useless in the first game, but is a good strategy in the sequel as they can be used to temporarily stun enemies to avoid encounters. There's even a whack-a-mole vase-throwing minigame on your cellphone, where you're encouraged to bean the rival's version-specific Denjuu while avoiding human characters.
Disc One Nuke: There are several secret Denjuu which aren't available in normal gameplay, unless you happen to know their phone number and enter it manually. Two of them begin at level 50 in the first game, while there is a level 30 one in the sequel. You can call any of them as soon as you receive your starting Denjuu, who is level 5.
The Human World, the place at the very beginning of the game, is larger than what you can normally see. It has plenty of unused buildings (albeit locked), including two large ones with unique graphics not seen elsewhere. 
Unused Super Game Boy features, including unused borders (the border depends on the version played), and some unused color palettes (although one is a glitchy completely white one). Even if the Super Game Boy functionality is enabled by hacking the game, there are still many unused color palettes that the game could have used. 
Some unused moves, although many of them are either identical to existing ones or are glitchy. This is also true in the sequel to an extent.
An unused shop, which presumably would have been near the cave in Ion Island, and two unused houses, which presumably would have been in Panses Village.
Electric Jellyfish: Lampgela in the first game is basically a jellyfish with a giant lightbulb for a head.
Elemental Rock-Paper-Scissors: Denjuu are classed by their habitat types, listed in the bootlegs as Hill, Sky, Wood, Lake, Sand, and Land. In the first game these were both offensive and defensive, going in a loop of effectiveness: any attack from a Sky Denjuu will do double damage to Wood, but half damage to Hill. The sequel attempted to alleviate this somewhat by introducing attack types of Normal, Fire, Water, Thunder, Wind, Rock, and Machine.
Engrish: All over the bootleg translation. Most infamous for "Some points of 24 lost!", and non-sequitur references to sedge.
Everything's Better with Monkeys: Waratah, a fluffy monkey-like Denjuu, features prominently in the first manga adaption as Matsukiyo's partner. While it starts out small enough to sit on a shoulder, it eventually evolves into a massive rideable baboon-like monstrosity. Also, it's notable for making monkey noises rather than speaking normally like every other Denjuu.
Evilutionary Biologist: In the first game, Sanaeba's goal is to apply the Denjuu's evolution abilities to humans. Presumably, this includes growing gun arms.
Fun Size: Most Denjuu are roughly human-sized or larger, but a few are small enough to ride on your head such as Punica and Waratah.
Game-Breaking Bug: Lots of these in the bootlegs, the main one being the inability to load a saved game. Some copies also lock you into an area in the middle of the game, rendering it uncompletable.
Game Over Man: Losing a fight when you only have one Denjuu in your phonebook, or to most bosses, results in a cute game over screen featuring the version-appropriate starter Denjuu knocked out on the floor. The player character is also shown in the sequel, leaning up against the defeated Denjuu.
Goldfish Poop Gang: Nerikara's political lackeys, the Kakuza Party members. They dress in bizarre animal mascot costumes, presumably to appeal to the Denjuu, and harass everyone by spamming their party slogan, "For The Bright Future!" Their Japanese name kakuza tou is a pun on kaku zatou, meaning sugar cube.
In Telefang 2, the trio Ellis, Vulcan, and Rumba, are also this.
Guide Dang It: Denjuu's elements are never disclosed until AFTER you've encountered them (and can check using the "status" option). This means that if your lead Denjuu is weak against the opponent's lead, you could very well get killed before your other Denjuu can arrive.
Harmless Villain: Nerikara, in the first game. A human who, for some reason, wants to run for Prime Minister of the Denjuu world and promises to build a curry restaurant if elected. He seems to be an annoyance rather than a bad guy, and just runs away whenever confronted.
Hello, Insert Name Here: While the original game lets you name the protagonist (and most Denjuu you've befriended), the bootlegs removed this option entirely.
Hopeless Boss Fight: One of the boss fights in the first game consists of every one of your attacks missing, while every one of his does maximum damage. You're then required to go hit up your rival for his Denjuu's number in order to fight the boss again.
Kid Hero: The protagonist of the first game is Shigeki, a 10-year old baseball fanatic who is rather unceremoniously dumped into the Denjuu's world with one of his friends when he happens to find a D-Shot cellphone, and immediately gets recruited by a giant turtle to start solving all of their problems. The sequel has Kyou, who enters the Denjuu world while the antenna trees are beginning to die out, in search of his missing father.
Lightning Can Do Anything: "Electricity did it" is the answer for every question you could have about the Denjuu world. Antenna trees emit electric waves which can cause teleportation, the Denjuu's special abilities are all powered by electricity—even those that have nothing to do with lightning, such as breathing fire or throwing a really big rock or shooting bullets out of their fangs—and it's assumed that the Denjuu are all spontaneously generated from the electric waves of the Life Tree. Replace all instances of "electricity" with "magic" and the series suddenly becomes much more plausible.
Mix-and-Match Critters: Many of the Denjuu are so bizarre that trying to figure out what exactly they're based on is nearly impossible. Whale-gators, fox-bees, tiger-weasels, and octo-phants are some of the more recognizable hybrids.
One of the Denjuu appears to be a lab rat with an eagle's head grafted to the back of it. Its description attributes this to experimentation by the Corrupt Corporate Executive.
Mons: Called Denjuu, meaning "electric beast", they were referred to as "electric monsters" or "e-mons" in the bootlegs.
Money for Nothing: Lack of money is pretty much a nonexistent problem since items are pretty cheap and you can get cash every time you win a battle, and even more just by running through the grass.
Monster Town: Justifiably, all of the towns qualify as this.
One Game for the Price of Two: In the model of Pokémon. There are about a dozen version-exclusive Denjuu in each of the games, notably the starting Denjuu (at least in the first versions, the sequel only has one starter) and the main rival Denjuu.
Party in My Pocket: Averted. Only one Denjuu is assigned to the protagonist's party at any time, where it is seen following him everywhere. Additional party members are called for at the beginning of every battle, where it may take them several turns to arrive because they're presumably at their respective homes when they're phoned.
Rare Candy: The first game had items which would boost a Denjuu's experience a great deal, if you gave them one of their favorites. Depending on the item, this could be exploited easily if they happen to be found cheaply in one of the shops.
Rewarding Vandalism: Somewhat subverted; while breaking vases can sometimes cause diamonds to spill out, collecting them doesn't actually add anything to your total. Tearing through grass, however, causes collectible coins and diamonds to fly everywhere.
Rocket Punch: Robot-cat Kaya has this as an attack in the sequel.
Secret Character: In both games, there are a number of Denjuu which are never available in the course of regular gameplay (14 in the first game, and 10 in the second, not including their evolutions.) Instead, their phone numbers could be obtained from a variety of sources such as tv commercials, chapters of the manga, and packaged with toys. All of the secret numbers were eventually compiled on Smilesoft's website.
Shout-Out: One of the items in the first game is Comic Bom Bom, a reference to a monthly manga magazine published by Kodansha Limited, which the Telefang manga appeared in. In the sequel, one of the special attacks features a rocket labeled "Natsume".
Socialization Bonus: Trading Denjuu between versions is the only way to Catch Them All. However, with branching evolutions of one-of-a-kind Denjuu in the first game such as the version-exclusive starters, this takes several copies of each game to accomplish.
The Lost Woods: Ixos Forest in the first games would send you in circles if you didn't proceed through the exits in a certain pattern. This pattern differed between the two versions.
The Maze: Several of the later dungeon mazes are frustratingly large, and the frequency of random encounters only makes them more infuriating.
Theme Naming: The majority of Denjuu in the first game were named after random plant genera, while those in the second game were usually named after bird species.
Theme Twin Naming: Netaro and Nejiro, taro meaning "first son" and jiro meaning "second son".
The Short Guy with Glasses: Shigeki's classmate Matsukiyo, who is accidentally transported to the Denjuu world with him. While he forgoes accompanying the protagonist in order to assist their monster turtle mentor, he will often phone with important news. Matsukiyo reappeared in the sequel, which takes place several decades after the first game, as a professor.
Turtle Power: Musa, some sort of rocky-looking turtle-dragon hybrid, is the Denjuu who apparently summoned the protagonist into the Denjuu world in the first game. He's the elder of Toronko Village, and is one of the Denjuu whose phone number is a secret.
Weasel Mascot: The giant striped weasel Denjuu Suguri is Miyo's partner in both the first game and its manga adaption, but he featured much more prominently in the latter.
What Measure Is a Non-Human?: Despite the fact that Denjuu are sapient beings with the capacity to form villages and befriend humans and use cellphones, Sanaeba has no problem with performing medical experiments on them, or trying to steal the power of their Life Tree in order to benefit humanity.
World Tree: The Life Tree is apparently where all Denjuu are born from, leading to a bit of Fridge Logic later when one ponders how Netaro and Nejiro can actually be brothers. Perhaps they fell from the same branch of the family tree?