The glory of URF mode is that there's very few bad champions, except those that have been artificially made so thanks to game-mode specific nerfs (RIP AP Skarner). When everything is broken, however, the deciding factor becomes individual preference, as a champion is only ever as strong as the person controlling them. Finding out what powerful champs fit your playstyle is integral to your success in URF mode, even now that the champion select is completely randomized.
Are you a long-range sort of mage that loves Bonucing Bomb more than you probably should? You'd love Xerath then, as his Arcanopulse has quite literally no cooldown on URF, meaning the endless barrage of inifinite-range poke only ends when your screen turns gray! Love showing off your tricky plays and talent for assassination? LeBlanc is one of the staple picks of URF, as her mobility and burst damage make her hard to handle. Enjoy frustrating your opponents until they quit the game out of sheer frustration? A certain chime gathering extradimensional entity might be just for you!
We polled the League playing members of our staff here at WWG about what their favorite champions to take out in URF are and got some pretty interesting (and some very predictable) responses. Check out their recommendations and maybe they'll inspire you to find a new URF main!