I've been monkeying around with Volibear since Sejuani is pretty close to permaban in Ranked Silver. He is pretty beast. Last night I made a Swain **** two crows when I flash Qed in on him from the river bush. If he hadn't of flashed instantly he would have been a dead bird.

I also solo killed a fairly fed Caitlyn while only having cloth armor and my runes for protection. Thank you The Relentless Storm.

For crowd control Volibear brings a displacement via Thundering Smash and a slow via Sky Splitter.

Rolling Thunder
Rolling Thunder is both fun and frustrating. It isn't an instant gap closer, which makes Volibear very kiteable. I find it most reliable when I'm already close my target or can combine it with flash to get close to them. If you can build into it early upgrading your boots with Distortion is probably not a bad route. I've also had good success combining it with the active from Turbo Chemtank especially if you can find an angle from which to flank your target.

Rolling Thunder does interrupt channeled abilities such as Katarina's Death Lotus. Yay for that.

You do need to be a bit cautious about who you toss and where you toss them. E.g. Don't flip a 500+ stack Nasus behind you if that puts him closer to your carries. Sorry about that Graves.

Majestic Roar
Magestic Roar is an interesting ability as it is, to my knowledge, the only AoE fear in the game. However it will only fear minions and monsters. This is definitely useful in the jungle as while feared the jungle creeps will not damage Voli. Primarily because of this ability Voli, with a leash and a health pot, can make it through an entire jungle clear without having to back.

For ganks, pop this after you flip them for the slow or if you can't quite catch them but can clip them with the AoE on this ability you can slow them in order to catch up.

In lane you could flip the enemy champion into your minion wave, pop this to fear their minions and then start autoattacking them. If they try to autoattack trade back they will take a lot of damage from minions, while you take none from their minions.

Frenzy

Frenzy does a heap of damage from the get go. The lower their health, the more damage it does. The more health you have the more damage it does. So you can build tanky and still dish out tons of damage.

When jungling use it after Smite for more damage. E.g. Auto twice, then Smite since it is an instant cast it won't interupt your third auto attack and then use Frenzy.

If you have two stacks Rolling Thunder will generate a third stack, so a nasty thing to do is to autoattak a minion or two to get your stacks up then if your target is close flip them with Rolling Thunder and then take a chomp out of them with Frenzy.

Thunder Claws

Stormbringer lasts for 12 seconds and procs when you auto. So it is kind of like the proc from Statikk Shiv you can just do it multiple times and it is limited to jumping to 3 targets.

Great for team fights and ending a fleeing enemy if they happen to be near a minion that you can autoattack.

It like Majestic Roar also does Magic Damage which can make Voli hard to itemize against.

When to Pick Volibear

You've got some health stacking tanks to murder. Your team can use a hard to kill bruiser/off-tank with decent initiation.

When Not to Pick Volibear

Nami, Vayne, Kalista, Janna are some of the champions I would try to avoid picking a Volibear into as they can really stuff up his initiation or simply kite away from you with ease unless you can catch them by suprise.

You also want to have a main form of initiation. Voli's by itself isn't good enough. After your main initiation Voli can go hunt down their carries to flip into your team and just generally cause havoc in the middle of the fight with Thunder Claws and Majestic Roar.

Jungle Specific

If you are against a jungler with fast clears you may want to invest in a Ranger's Trailblazer as this will let you clear camps faster. I ran into a Shyvana that was eating my lunch as far as clearing, so this is strategy that I'm going to try the next time I run into a jungler with fast clears.

Runes and Masteries

I've only ran 21-9-0 on Volibear so far, but I can see a case for 9-21-0, and or 6-21-3 if you want the extra movement speed from Utility. Going the 2nd two routes will slow down your jungle clears and make you more reliant on your team to get kills, but they will allow you to tank even more damage than you can going 21-9-0 assuming your team needs you for that.

Atk speed lets you generate more frenzy procs, though the cooldown is fairly high on the active portion of Frenzy, so there is probably a happy medium that can be achieved between Atk speed and other stats if you need them.

Atk speed marks, Armor seals, MR glyphs or scaling MR glyphs, and Atk Speed Quints are a viable path.

I could also see running some CDR glyphs to get Frenzy off cooldown faster.

Alternatively, running Atk speed Marks, Health Seals or scaling Health seals, MR glyhps or Scaling MR glyphs, and Armor Quints, could also be a viable option.

Other
Got some good tidbits from this page Voli-Strategies, some of which I've woven through the analysis above.