Volibear is pretty much the greatest champion in the entire game. Not much else to say other than he is a bear, which makes him the best.

I grabbed all defense masteries because BEEFY equals good.

Max Rolling Thunder by level 9 as it's going have the most utility for this build. Next, you'll want Frenzy maxed by level 13. Grab an early point in Majestic Roar at level 4 and max it last. Grab points in Thunder Claws whenever possible.

Get 9 Marks of Vitality and 9 Glyphs of Vitality for health. I chose health per level because flat health won't benefit you as much in either early or late game. Get 9 Seals of Regeneration and 3 Quintessences of Regeneration for health regen. Again, I chose per level instead of flat because it'll benefit you more.

Grab Doran's Shield for early beefiness. Next you'll want to grab Boots of Speed, which build into Boots of Mobility. This will give you a good amount of movement speed with which you can bum rush those doods. Building into Warmog's Armor, you'll want to grab the Regrowth Pendant first for some health regen. Next you'll want to grab the Ruby Crystal for cheap health. After you get the first Warmog's, you can build your second in a multitude of ways. If you have enough gold to grab the Giant's Belt, get it before any of the other things. Otherwise, I'd recommend the Regrowth Pendant first.

An alternate build choice might be to go for a single Thornmail after you get the first Warmog's Armor.

Not much to discuss. Heal gives you health, Ghost gives you speed and slippery bear ninja moves.

I think the build speaks for itself, it's just too good. I'm surprised that Volibear hasn't been flatout banned for being so good. Basically, you just be a bear. You walk around killing things, doing bear stuff, and you NEVER DIE EVER. Gank in your lane? I'M A BEAR AND I DO WHAT I WANT. Fling them at your turret and proceed to do bear things to that fool. You can pretty much defend endlessly forever, cause you got to protect your cubs with your INFINITE HEALTH. Also, you're quick as all get out. Someone pushing a tower? Loop around through the jungle and push that kid into the tower. They'll be all, "What was that?" And you'll be like "RRAALKHFHAAHSADA", cause you're a bear.