I start with four of them and would be happy about more.

There once was an archer named Ashe,
who killed little minions for cash.
But stopping the fun
was a wee little stun
of an Udyr who still had his flash.

From the distance is shooting Kog'Maw,
striking the carries with awe.
But lacking a breakfast
he wasn't so steadfast
an empty stomach 's his only flaw.

On the top lane is working a Heimer,
checking his new turret's primer.
Then out of the thicket
comes LeBlanc the wicked,
and starts his reanimate timer.

Standing alone on the lane,
is idling the powerful Swain.
First to him came Trundle,
then Poppy, then Rumble,
all of which are now slain.

There once was a gem knight named Taric
Who would run around, Shatter, and Radiance
Absolutely fabulous
All critics are baseless
'Cause his gems are truly outrageous

Karthus had been wrecking face,
So when he came back from his base,
He didn't go far,
He simply pressed "R"
And pentakilled us for the ace.

My teammate was a free-week blitz
Who couldn't keep track of his wits.
Out of panic and fear
He pulled an Udyr
And we told him that he should just quit.

I once fought the champ they call Shaco
Two-shiv poison jack-in-the-box jack-in-the-box
Clone deceive two-shiv poison jack-in-the-box
I hate Shaco.

There is a poor woman named Evelynn,
Whose haters are ranting and revelin'.
Riot must fix
Her being bad picks,
Or else good old Eve just may never win.

I couldn't resist to make more...

There once was a knight named Garen,
his opponents plead him to spare them,
but he turned around
and with a loud sound (DEMCIAAAAAAA)
started to whirle and to slay them.

Lux is a lady of grace or
at least that's what she thinks she stands for.
But belive me in summon
she is rather common
when she is firing her Lazor!

There once were a dog and a croc
who eagerly joined the champ-flock.
To come from a desert
means cold is a hazard
and tuning them into an iceblock.

Imagine the teenager Annie
Who unquestionably has a nice fanny
And beautiful hair...
OH ****, FLAMING BEAR!!!
Now I'm dead just like my Granny

Broken blade wielding Riven
Who once was all power driven
Now in exile she stays
To pay for mistakes
Reforging her spirit from within

Alas poor Yorick, nothing rhymes with him.