I honestly don't find I use Relentless much. I usually prefer to have my rotations more tightly controlled, and having extra turns messes that up.
That being said, since it's low probability, it's best used in places where you have a lot of turns to go through, so you'd want to focus on champs you're using pretty much exclusively for dungeons or faction wars. Within that set, you're probably best off having it be on champs that have specific skills which are useful to have on low cooldown. Scyl is a common target - every extra turn she gets heals your team, and lets her use her AOE stun more often. Siphi may be a good target as well.