Hi my name is sologank. This is my first guide, so please dont be angry if there are some mistakes :) Currently i am Gold 1 and i think i am decent with Udyr and really enjoy playing him, so i decided to do a "Guide" on him. Hope you enjoy, pls first try the Guide out before you Vote it, thx!
This guide is not finished yet, I will try to do some visual upgrades and of course add more chapters, stay tuned!

Smite - You need that your a jungler. Objetive Control (Buffs, Dragon/Baron).
Ghost - In combination with Udyrs movementspeed, Ghost is very nice for catching people running away etc.
Flash - Higher cooldown than Ghost, but you can get over Walls. I dont really think Udyr needs flash, he's quite fast if you have these Masteries and Runes i recommend.

Attack Speed Reds - Attack Speed is very good on junglers! = Better clear times, Bigger dueling Potential and Udyr's Phoenix Stance fire will be activated faster. ("Every 3rd attack, Udyr engulfs enemies in front of him in flames")

Armor Yellows - Pretty Standard. You take less damage from early fights and the jungle camps.

Magic Resist per lvl Blues - Magic Resist is not so important early in the jungle. But in mid/lategame, a bit of MR will be good.

Quints of Movementspeed - 4,5% Movementspeed doesnt sound alot, but in combination with Udyrs passive (Monkeys Agility) and the Masteries (Wanderer, Nimble), you will get about 10% more Movementspeed! That helps you out quite alot.

The Standard jungle 9/21/0 or 0/21/9 isnt bad but 0/9/21 is the best Masteries setup for Udyr in my opinion. So why do i put 21 points in Utility? EXPLANATION:

(9) Defense:
1/1 "Summoners Resolve" - Extra 10 Gold if you use Smite. Just personal preference.
4/4 "Durability" - Core on Bruisers/Tanks. +108 Health at lvl 18.
3/3 "Hardiness" - 5 bonus armor, why not.
1/1 "Veterans Scars" - Bonus 30 health, this helps you a little bit early on.

(21) Utility:
3/3 "Wanderer" - 2% Bonus Movementspeed. In combination with "Nimble" its 5%.
2/3 "Meditation" - Little bit Mana Regen. You can also but those 2 points somewhere else.
3/3 "Mastermind" - 10% Summonder CD reduction!
1/1 "Runic Affinity" - Must have on buff dependent junglers! Very helpfull.
3/3 "Vampirism" - Gives you a little bit more sustain.
1/1 "COOOKIE" - Personal Preference. Free health/mana pot.
4/4 "Awareness" - 5% More XP
3/3 "Intelligence" - CD is always good.
1/1 "Nimble" - 10% more Movementspeed with "Wanderer" and your Movementspeed Quints!

So the main reason why I put 21 points in Utility, is the huge bonus Movementspeed!
If you think with 0 points in Offense, you dont do enough damage, thats wrong. Udyr still does alot of damage in 1v1 or when ganking, even if he has 0 points in offense!
And with my recommended item build, you dont need 21 points in defense because of the Ancient Golem tenacity, Health Items and the Boots of Swiftness you are tanky enough.