Oh, you had to make this topic... Alrighty. Let's begin. I'll start with some RPG cliches that work in Pokemon.
Get up, Kid!
Trainers often begin the first day of their career by oversleeping, being woken up by their mother, and being reminded that they slept so late that they missed the meeting with the Professor.
He's Proud? But Daddy Is... Where Is He?
Most Trainers only have a mother and no father, either because they walked out on their nagging mother or because they went crazy from flashbacks of their Pokemon adventure and took their own life.
Professor Forestman
All Professors are named after trees. If there is ever a Trainer with a last name that is a tree, then he or she must at some point become a Professor.
Logan's Run -5
At exactly the age of 10, every child is required by law to receive a possibly feral pet and take a journey out into a dangerous world filled with wild, lethal, and often rabid creatures in order to prove themselves as adults. Fortunately...
That Episode of House With the Chicken
Trainers don't have to fight said creatures themselves. They can let their pets do all the fighting for them. After all, better them than us. Unfortunately...
The Inexperienced Professional
Regardless of how good Trainers get at raising Pokemon, they will never gain a single level.
The Compulsories
Fire, Water, and Grass are always encountered, and almost immediately. But Steel, Dragon and Fighting aren't encountered right away. That would just be silly.
Crono's Complaint
The less the Trainer talks, the more words are put into his mouth, and therefore the more trouble he must get into through no fault of his own.
If It's Not Nailed Down... (Kender Rule)
All Trainers are professional thieves. They can walk into just about anybody's house like the door wasn't even locked. They just barge right in and start looking for stuff. Anything they can find that's not nailed down is theirs to keep. Trainers will often walk into perfect strangers' houses, lift their precious artifacts, and then chat with them like they were old neighbors right before heading back out with the poor guy's family heirlooms under their arm. Unfortunately, this never works in stores...
Dimensional Transcendence Principle
Buildings are much, much larger on the inside than on the outside, and that doesn't even count the secret maze of tunnels in the basement.
Meowth, Whatsit?
If you ever encounter a cat with a Brooklyn accent, chances are you'll have to see it at least ten more times over the next month.