So when Rengar and Khazix are both in a game together on opposing teams and hit level 18, the side quest "The hunt is on!" begins where they have to kill each other. Honestly this has proved to be a pretty involving part of the game when it's two teams against each other, but two specific players have a greater need to kill each other and target them (as long as they also contribute).

Does anyone else think doing this theme with other champions would be a good idea, and if so what champions? so far suggestions I've received include Darius Vs. Draven (blood brothers), Leona Vs. Pantheon (Honorable Death), and Morgana Vs. Kayle (holy Spirits). please comment if you have any more ideas, or if this would indeed be an interesting concept that could be explored more!

yes please

Soraka vs. Warwick (Unfinished Business)

Riven vs. Singed (Back from the dead)

Just a couple I can think of.

Ashe vs Sejuani (Icy Conflict)

Yi vs Wukong (Master vs Disciple)

Tryndamere vs Ashe (True Ruler)

Would be a pretty awesome idea the only problem is that they would need to be very precise just as 'The Hunt Is On' quest is. It requires late game and for Rengar to be at least fairly fed. On top of that they both fulfill remotely the same role and are most likely on the same lane (but not always).

A lot of the posts I've seen in this thread don't really have the same diversity in the champion's skill sets and roles to match-up with the lore, e.g. Warwick vs Soraka. Neither have a specialist item for themselves, they fulfill entirely different roles throughout the game, will have largely different stats throughout the game (Soraka assists, Warwick kills and assists) and would be vastly imbalanced in a 1v1 scenario.

To add things like this in to the game would either require some incredibly clever thinking or a lot of new items / role diversity for the champions involved.

What about a Jarvan/Garen one? they are both normally top laners
Or maybe Syndra/Oriana, no lore, but both play with balls and are normal mids n.n

Aren't Tryndamere and Ashe in love? Why would they fight?

Sejuani is the one who has beef with Ashe, not Tryndaemere.

Also for the Darius/Draven, just because they have a connection doesn't mean they'd have a quest to fight each other!! Why would Cassiopeia ever want to attack Katarina, and the same with Garen+Lux? And for the poster above me.... Garen has sworn to protect J4; his prince. He has saved his life before from Urgot when he was still "alive". Why would they ever need a special quest to attack each other??
If you want rivalries, think of ones that actually make sense:

Nasus vs Renekton
Diana vs Leona
Swain vs Jarvan
Quinn vs Talon

Hopefully they add this with Talon and Quinn: It seems like they may, with all the lore Ironstylus is setting up with "Demacia Needs Heroes"... I like it!!

They don't have a rivalry, WANT to kill each other. But yeah I agree with the op they should add more of these types of quests, another type of quest that could also be added is if to allies are on the same team they could have a Race To Level 18 like Garen and Xin Zhao could race to prove which is the better fighter, same if Wu and Yi are on the same team. Also Zilean could get a quest at level 6 to successfully save an ally with his ult, but that could be to easy if teams just set it up.