Can Udyr / Others have a real "Ultimate" ability?
I don't know how specifically it could be done for Udyr, but I think these awkward champs that don't have Ultis or key moments in their kit are kind of an out-dated concept.
Monkey's Agility doesn't feel very useful at all at any point in the game. Plus, Tiger Stance is what you do for attack speed, Bear Stance is what you do for move-speed. We could replace this passive with something more interesting to give Udyr a "key moment" in his gameplay.
An example of what I'm talking about is Corki's new Special Delivery. He was another champ with no ulti but got this new thing on his kit. Yeah his missiles unlock at lvl 6, but after that it's like having 4 basic abilities.
Whether it's a more interesting passive on a big cool-down like Kindred, a new "super" upgrade to an ability like Corki, an item you somehow work towards buying or buffing up, something, anything!
Jayce is definitely a candidate for buying / upgrading an item like Viktor. Nidalee could have something where her goal is to clear out every camp in the jungle. Elise could have the ability to turn a cleared camp into an allied "Spider nest"