Old Rod
Magikarp encounters a bit of fruit under water. You can decide whether or not to approach it. If not, you get Jump Power. If you do and you succeed, you get more Jump Power. If you do and you don't succeed, you lose Jump Power
Nugget
You receive Coins scaled to your level
Is It Treasure?
You find a Poké Ball in the road. You can choose if Magikarp opens it or not. If no, you will receive Jump Power. If you do, there's a chance of finding Coins or a Voltorb which will explode and make you lose your Magikarp
Our Eyes Met
A strange man appears. You're asked to look into his eyes or not. If you don't, you get small JP. If you do, you have a surprise battle with him and you may lose JP, or you may earn a Support Candy
Out Of Nowhere...
You find a tree with berries on. You can choose if Magikarp should jump to get it or not. If no, you will receive Jump Power. If you do, you can get Jump Power if Magikarp succeeds or a Pidgeotto appears and you lose your Magikarp
Idol Riches
The mayor appears with compliments. He then gives you a Training Soda.
Massage A Karp
Mayor Karp will visit and give you words of encouragement. You gain a Training Point
Everyone's Hero
A fan comes to ask for words of encouragement. You gain a Training Point
Roddy Tackle
A fisherman comes and offers words of encourangement. You get Coins
Unsinkable Magikarp
A fan comes and gives encouragement after a loss. You gain a Training Point
Go, Magikarp, Go!
Mr. Yoso will come up with a message from a fan. It will be accompanied by coins.
All That Glitters
A mysterious sparkling item appears in the ocean. You can choose if Magikarp investigates or not. If no, you get Jump Power. If yes, you have a chance of either getting Diamonds or Magikarp could lose some gained Jump Power from its activity.
Jumping Lesson
You get approached to enter a special Jump Course. You can decline or enter at a risk. If you decline you get Jump Power. If you succeed, you get a lot more Jump Power. If you lose, you lose coins
Mystery Drink
A scientist approaches you with a new miracle drink. You can decline or test the drink. If you decline, you get Jump Power. If you accept and succeed, you get Training Points. If you lose, you lose some of your gained Jump Power
Magikarp Adrift
Magikarp moved too far away from you and needs to find its way back. You gain Jump Power if you tell it to wait, or you may lose Jump Power if you tell it to search
Snoozing With Snorlax
Your Snorlax is blocking the path while sleeping. Magikarp goes to sleep on its belly and you collect full Training Points
Tag Battle
A Pidgeotto attacks and Pikachu steps in to defend Magikarp. You gain Jump Power
Showing Off Magikarp
A fan comes by and wants to see Magikarp Jump. You get a Training Point
Sage Advice
After losing, another Magikarp will show up and offer some advice. You will gain Jump Power
Trade For Gyarados
A scientist approaches you and asks to trade your Magikarp for Gyarados. You automatically decline, resulting in receiving Jump Power
Lost Luvdisc
A Luvdisc will appear and ask for your assistance. It will give you Diamonds.
Easygoing Slowpoke
After having lost in a league match and going to training, Slowpoke will appear and will give a LP Restore
Watch and Learn
After training, you will be approached by a character who commends you on your training. You'll get give one free training regime
Slacker Magikarp
Magikarp is feeling weak and wants to skip training. If you don't scold it, you gain Jump Power. If you scold it, you may gain Jump Power, Training Points or lose gained Jump Power
Macho Karp
A scientist will request help with an experiment. If you decline, you get Jump Power. If you say yes, you have a chance of losing your Magikarp as it evolves into Gyarados but if it works then your Magikarp's maximum level will increase by 1
Fan Mail
Mayor Karp delivers a letter from a fan. It gives you a LP Restore
A Challenge
Mayor Karp delivers a letter from your next opponent. It gives you additional Jump Power
Many Wise Words
The mayor appears and gives various anecdotes about Magikarp.
Research Money
After a successful league battle, after collecting many patterns, Mayor Karp will come and offer you Coins for raising all the different Magikarp
The Fun Way Home
Your Pokémon will meet up after training. All your Pokémon's skills are restored
Cheap Cheap
A mysterious man will appear after training and offer you a prize. You may run, which results in JP, or you may accept it. If you accept it, you may lose coins or you may get a Training Soda
Name Rater
After training with a nicknamed Pokémon, a Name Rater will appear. They will give you Diamonds
Say Cheese!
Mayor Karp appears and offers to take your photo. Magikarp is enthused by this and gains Skill Points for a random Support Pokemon and saves the photo
500 Coins
A man comes up to you to sell you a Magikarp for 500 Coins, before you can accept he gets caught and you gain JP.
Dumpster Diver
You can choose to leave, where you'll get JP or enter the dumpster. If you fail, you lose JP but if you succeed then you get a Skill Restore
A Mysterious Feather
When heading home, you find a feather in the path. You can run away from it, where you get JP or you can investigate. If it succeeds, you get JP but if it fails, your Magikarp loses JP.
Let's Be Friends
When you have Mimikyu, after training you will find yourself in a forest. You have the choice to flee or you can explore the forest. If you explore, you may get lost and lose some JP or you may find Mimikyu and gain a Power Up.
Is It Feebas?
Feebas will sometimes swim into the aquarium. Tap it for Jump Power
Food Fever
Manaphy will sometimes swim into the aquarium. Tap it to start a festa where lots of Pokémon will swim in and leave you food.
Be Gone!
If you click the TV and cancel 7 times, it will break. Then, fix it by clicking and cancelling 7 more times. This activates an event after training where you meet a ghost girl who orders you to be gone. Afterwards, your Magikarp's maximum level increases by 1
This event can only be activated once
Hop, Skip & Whump!
Keep jumping in the aquarium and eventually a Pidgeotto will swoop in and take your Magikarp
This event can only be activated once
You're No Magikarp!
When fishing a new Magikarp, you accidentally fish up a Dratini. This is done by re-fishing four different consecutive times (total of 210 Diamonds spent) after fishing a Magikarp. You get given a Skill Restore.
This event can only be activated once
You Can Do It!
After losing three times in a row, the Man of Mystery appears and offers encouragement. He gives 3 LP Restores.
This event can only be activated once
Adios, Gyarados!
Tap your Magikarp repeatedly to break the Everstone. On the next level up (after Level 20), it will evolve into Gyarados. You lose the Magikarp
This event can only be activated once
Let's Push It!
If you go into the Decoration list and tap the Bronze Eevee, you will press a button and get a Skill Restore.You need to have checked Event List's #40 in the event list to activate it
This event can only be activated once
Transforming Magikarp
Sometimes, you will see a rod facing the other way when fishing your Magikarp. If you select this rod, you will hook a Ditto posing as a Magikarp. This unlocks the Ditto Cushio in the shop
This event can only be activated once
Events 40-46 have unknown Unlock Methods. I can't include unlock methods, as it would be too many characters. You can find them all in the links to the event pages, however.
Hope I helped!