What are the best champ jokes?
My personal favorite is heimerdingers joke.
"why do chemists call helium, curium, and barium; the medical elements? Because if you cant helium or curium. You Barium!!!" 
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"I ate an optimist once but I couldn't keep him down."
"I tried to silence my nother once, boy did I regret that"
Doesn't make much sense now though lol.
"Sometimes this anchor just weighs me down..." -Flies into the sky- "Ladadee, ldadadoo, ladadaaa"
"You can't milk those."
Simple. Understated. Open to interpretation. Hilarious. Vaguely suggestive. Spoken by a cow. All the ingredients of a masterpiece joke.
"A man , a woman and a yordle walk into the sun. They die. Because it burn them alive "
Azir's joke is the best in the game.
Cooo, cooo..... cooo..... cooo cooo, cooooOOOOOO!
"I guess you're expecting some sort of unBEARable pun?"
"Our seasons are reversed. My spring, your fall!!" Need some ice to cure that BURN!!
I like 
's joke, "Why can't I get a straight answer its always 'Oh no stop hitting me' or 'Ow my face'".
's old joke.
https://www.youtube.com/watch?v=eunFNjaQ1PU
Blackfrost 
's epic egg laying.
Not sure if its his joke or not but i heard it while laning against him.
"I've seen your death, it was painful."
-
D:
It also depends on the localization. I play in italian, and I think the translators did a great job with and 
jokes.
Heimer says something like "What's the difference between a noob and niobium? The atomic number, of course! If you are noob it rhodiums your chrome* if you lose"
- in italian this sounds very much like a colorful way to say "whine"
Yi does a pun on "a spoonful of sugar helps the medicine go down": "go down" in italian is "va giu", and he says "wuju" instead. xD
We have learned of Spin to win now none can stop us, It was a trick!
(eternum) skin
"two birds with one stone? have you met my parents?"
"Wanna know why me Roger is so Jolly?
Edit: not jokes yet could have been replacements for his
"Look what trawled out of the bunghole!" "Yo ho ho, and a bottle of... rum!"
knock knock...
Her jokes are amazing.
"Joke? what do you mean?"
For $2.95 per minute, i'll leave you breathless
Dafaq riot, you made Janna a prostitute?
Obviously
"Only time I have a drinking problem is when I spill it!" 
You can't milk these! Always gets me to laugh.
I find Rammus to be the most charismatic of all the League characters- his joke is easily my favorite.
This isnt a joke, but i find it funny when heimer says "Back you dirty ape
, Back!"
"Yes, that was a banana (giggles). No one expects the banana." 
Timing the joke after killing someone with the banana though
This has been my favorite since before season 1.
"Seriously, are you really asking a giant demon bird for a joke?" 
Nobody understands me; they called my work a hack job!
Time flies like an arrow, Fruit flies like banana
I've seen your death. It was painful
i love both of these and his laugh too, overall one of the best VO's in game imo
"DEMAGLIO!" 
"I'm gonna crush your dreams... They're in your skull, right?"
"You got a problem with me? Join the club!"
i got trundle brcuase he was so funny XD
"The worst part of losing a blade is trying to trace back all my stabbings."
I have a terrible memory so this always appeals to me
every time a says that i say "BOO!" hisses