Udyr is not your tipical "follow this build" champion. For starters - he is exceptionally melee with no ranged attacks, unlike other melee champions with leaps, charges, and throwing thingies. You don't have the luxury to harass with Udyr, thus getting close to your enemy without advantage is not recommended (ex. early game the turtle shield is a big advantage, especially against Zilean's bombs).
As for items, rule of thumb - build according to your enemy and what your team requires: Udyr can be anything, from a tanky initiator to a tower pusher and champion killer. Going for a more tanky build you do not deny Udyr damage, he is still able to put up a good punch.
Udyr is the carries' carry.