One strategy that works very well in almost any Pokémon game is simply using only one Pokémon in battles. While you're supposed to be using a balanced team to counter the Pokémon that are strong against your starter, by simply using the same 'Mon over and over, it becomes so powerful that even super-effective hits deal almost no damage (and that's assuming they manage to hit you at all). Not until Pokémon Black and White was this strategy finally nerfed; your experience gains are based on the level difference between your Pokémon and the Pokémon you're fighting, so training just one Pokémon isn't really viable, since they'll be getting crap Experience in no time. It's important to note that you WILL get a lot more EXP at the same level though, making getting early levels much easier. And later in the game, you can still be so overleveled that you don't NEED more... It's not uncommon to see a level 43 or so Emboar (usually used because it has a great movepool and decent all around offenses) before the fourth Gym, when the Gym Leader uses level 30 at the most. GenerationVI reverted back to the experience distribution of the previous games... and introduced the Exp Share which makes it even easier to turn your party into a One-Man Army. Thankfully, Pokémon Sun and Moon gave players a compromise, with the return of Generation V's experience distribution and Generation VI's Exp Share. A One-Man Party, while still more feasible than it was in Generation V, is once again no longer viable.
The single easiest way to get through any game is by having a friend who has already beaten the game and is willing to trade powerful mons. The first Gym Leader's level 15 or so Pokémon aren't exactly a match for a level 90 juggernaut, are they? To attempt to prevent this, the designers include the badge system; Pokémon not caught by the player will usually ignore them (doing things like sitting around, even sleeping in the middle of the fight) if they are above the level designated by the player's badges. The problem is that: 1. the Pokémon only has to listen to the trainer once, while in the meantime the opponents aren't capable of doing anything at all thanks to the super-Pokémon's ridiculous defenses, and 2. the badge system seems to think that the Trainers are much stronger than they are (for example, getting the fourth badge makes a traded Level 50 Pokémon listen to you, whereas the final boss has Level ~60 Pokémon in an average game). Even easier is if you have a friend further in the game who has a bit of patience. Trade them your Mons and have them level them up on the higher-leveled Pokémon late in the game (along with the boosted EXP for trading), and then trade back when they're sufficiently leveled. Then you won't even have to worry about the Pokémon ignoring you occasionally, as your own will listen to you no matter which badges you have.
If you battle competitively, RNG abuse is probably your best friend. It allows players to use computer software to do some calculations, then set their DS's game clock to the right point and locate an exact right moment to catch or hatch flawless stat and even shiny Pokémon with relative ease. However, no external devices ever touch the game itself, meaning that many players do not consider it hacking.
Pokémon Stadium. Go to Pika Cup with a Level 20 Charmeleon, Dratini or Arcanine that knows Dragon Rage from a TM in Red, Blue, or Yellow and see what happens. It got nerfed on Stadium 2's Little Cup, though, where SonicBoom and Dragon Rage will always miss.
Wonder Trade in Pokémon X and Y can become this, if you get someone's level 50 or 60 mon early in the game. You will deal with the disobedience problem, but even attacking every other turn can be enough to Curb-Stomp Battle if it's a good Pokémon.
Far more likely, you'll get a "breeding reject"- a level 1 leftover Pokémon from someone's breeding project. These Pokemon might be species you can't get until much later in the game (or even ones that can't be found in the regional dex). Usually these mons have good Natures, perfect IVs in most of its key stats (or if you're very lucky, all its usable ones), great egg moves, great abilities (hidden or otherwise), and an experience point bonus, and they'll listen to you due to being very low-leveled on top of all that. Basically these mons are often far better then other monsters at the beginning of the game, even your starter, and may remain useful when you want to start your own breeding project much later on.
If you're willing to shell out the extra cash for Pokémon Battle Revolution and spend five minutes finding the proper codes on the internet, you can get your hands on two free Mystery Gift Pokémon for any DS game: Electivire and Magmortar. Both came stacked at level 50 with great physical and special stats (respectively), in addition to some hard-to-get moves that between the two, covered pretty much every type in the game. The only requirements? Have a Pokedex, be near a Poké Mart, and have access to Mystery Gift, all easily done through less than an hour of playing and some more net-surfing. Oh, and, have at least four Gym Badges, or they will disobey you. Together, these two could carry you to the Elite Four, no sweat. And if you actually did some work to win at the Wii game? Say hello to surfing Pikachu!
Inver, the Inverse battle specialist on Route 18 in X and Y and in Mauville City in Ruby and Sapphire, gives out a daily reward whenever you defeat him. The more "super-effective" (that is to say, what would normally be non-effective) attacks you pull on him, the better the prizes. Of course, since Normal type is a Game-Breaker here, one can simply spam False Swipe over and over again instead.
The Poke Bank completely trivializes trading pokemon. You can load up all your pokemon from Pokémon Black 2 and White 2 and transport them into Pokémon X and Y, and your pokemon from both games into Omega Ruby and Alpha Sapphire, letting you start your adventure with all the freshly hatched shiny pokemon you spent so much time breeding, or the level 10 Tornadus, Landorus, and Thundurus you can get in the Pokemon Dream Radar game. In past games, you at least need to capture a few Com Mons first just to have trade fodder to get a few of your pokemon over. That, and the trading process itself, takes some time to accomplish. Starting the game with every pokemon already caught, and the Oval Charm in your possession as soon as you get your first gym badge, makes things a lot easier. The only caveat is that you have to get to a PC to actually use them; while X and Y don't provide a PC until Santalune City, forcing you to go through the first couple of routes and Santalune Forest with your starter and whatever you catch, in ORAS you can get to a PC as soon as you're past the (short) first route right out of Littleroot. With the upgrade to Gen VII, you can skip Gen VI entirely and transfer monsters from a Gen V game directly to Gen VII.
In Omega Ruby and Alpha Sapphire, specifically Omega Ruby, during the end game segment, when Groudon surfaces and the sun begins beating down on everyone, the Desolate Land conditions are active until the plot resolves. This would normally sound like a pain, but it is actually great for raising Fire-type Pokemon; it is quite literally possible to surf around the entire East coast of Hoenn and battle every trainer in the water. Watch while their water-type moves evaporate in the extremely harsh sunlight, leaving your Fire-type untouched, and you mow them down with any Fire-type move of choice. Maybe a Solar Beam if you're feeling particularly sadistic.