Oh Arcanine, I remember back in Gen 2 when I naively thought high total base stats made a good Pokemon and how surprised I was when I saw its total. Obviously I know now that it takes a lot more than that to be good in battle, but Arcanine is still arguably one of the best Fire types out there because of said high stats, access to good abilities, and surprisingly wide movepool both offensively, defensively, and in terms of utility. One of the great things about Arcanine is that it could be anything you want on your team. A physical sweeper, a special sweeper, a mixed sweeper, a defensive status inducer, a late-game cleaner, and I'm sure you could even run a weird set no competitive player would think of using. Honestly its difficult to use Arcanine improperly because of this, and that's impressive in of itself.
Abilities:
Intimidate: Lowers the attack stat of all opponents on the field upon switching in. Arguably the best of Arcanine's abilities, this ability is part of the reason it works as a defensive Pokemon and even on offensive sets being able to sponge physical attacks better is never a bad thing, especially with doubles becoming a popular format now.
Flash Fire: Fire attacks against the user (Including Will-O-Wisp) inflict no damage and increases the power of the users fire attacks by 50%. Not a bad ability as being able to switch into anticipated fire attacks or burns allows Arcanine a free switch in and gives it ready ammunition to strike back in full. But where this ability only works with fire attacks, Intimidate works every time you switch in, so Intimidate is the better option.
Justified (Hidden): Increases attack of the user by 1 stage every time it gets get by a dark attack. Even more situational than Flash Fire though at least the power boost applies to all physical attacks and not just fire attacks. Hypothetically you could use this ability in doubles alongside a Pokemon with Beat Up to rack up the attack boosts, but Arcanine's best physical STAB takes a chunk out of its health and the added damage from Beat Up doesn't help with longevity. Intimidate is just easier to use all around.
RK9 Unit (Mixed Sweeper)
Ability: Intimidate
Item: Life Orb
Nature: Naive
EV's: Attack: 252 Sp.Attack: 4 Speed: 252
Moves:
Flare Blitz
Extreme Speed
Close Combat
Overheat
A fairly straightforward set. Flare Blitz is the strongest move at Arcanine's disposal but trainers should be mindful of the recoil when combined with the Life Orb as health with fall off pretty fast. Extreme Speed picks off weakened targets with strong priority as well as faster and frailer targets. Close Combat (Not sure how a 4-leg creature can use this but whatever) offers the best coverage and damage of Arcanine's many offensive options albeit at the cost of defenses with each use. Finally there's Overheat which targets physically defensive Pokemon that can take a hit from Flare Blitz and unlike Flare Blitz does not come at the cost of its own health, and the special attack drop is manageable with a simple swap out (This also gives Arcanine a chance to use its Intimidate ability again).
The Pound Hound (Physical Sweeper)
Ability: Intimidate
Item: Choice Band/Life Orb
Nature: Jolly
EV's: HP: 4 Attack: 252 Speed: 252
Moves:
Flare Blitz
Extreme Speed
Close Combat
Wild Charge
Pretty much the same as the above set only with more coverage and power with sole physical investment. Flare Blitz is still the main move (Again watch the recoil), Extreme Speed has high priority and picks off those hanging on by a thread, Close Combat has the coverage, and the new slot goes to Wild Charge which targets Water types that think they have the upper hand (But again...recoil)
It's Always Sunny in Philadogphia (Special Sun Sweeper)
Ability: Intimidate
Item: Life Orb/Leftovers/Firium Z
Nature: Timid
EV's: HP: 4 Sp.Attack: 252 Speed: 252
Moves:
Fire Blast/Flamethrower
Solar Beam
Morning Sun
Dragon Pulse/Hidden Power (Ground)/Sunny Day
I'll admit Arcanine's special movepool is not as wide as its physical one, but I'm giving this a shot anyways, and at least this set does not have any nasty recoil moves. With the help of some sun from its teammates, Fire Blast is Arcanine's main power move but can be swapped out for Flamethrower if you want something more reliable. With sun support Aracnine can also spam Solar Beam allowing it to punish the Water and Rock types it would otherwise have difficulty with. Even without investment, Arcanine has good natural bulk and intimidate also helps compensate in its defenses, so running Morning Sun to keep it healthy is a good option to increase Arcanine's longevity. With sun up the recovery move even jumps from 50% to 66% of max health restored so its a good option all around. The final move is a toss up depending on what you want. Dragon Pulse provides good neutral coverage against threats that resist both your STAB and Solar Beam, Hidden Power (Ground) is more prescriptive in handing other Fire types that resist both attacks (Especially Heatran), or you could set up the sun yourself with Sunny Day which if used in tangent with a Z-Crystal can boost Arcanine's speed and make it even more threatening (Or you could always use an Inferno Overdrive STAB with the sun to instantly reduce key threats to vapor if you prefer). Really, the item choice is ultimately down to whether you want better longevity or greater power.
The Majestic Beast (Defensive Utility)
Ability: Intimidate
Item: Leftovers
Nature: Bold
EV's: HP: 252 Defense: 148 Sp.Defense: 108 (This is just a balanced EV set I like to use for all my defensive Pokemon, go on and judge...)
Moves:
Flamethrower
Will-O-Wisp
Morning Sun
Toxic/Roar/Fire Spin
(Looks at above posts) Shoot, someone beat me to it...ah well. Might as well reiterate.
Arcanine works surprisingly well as a defensive stall and status inducer thanks to its natural bulk, intimidate, and access to Will-O-Wisp. Flamethrower keeps the Taunt users from ruining you and still offers consistent and powerful damage thanks to Arcanine's good offensive stats, Will-O-Wisp whittles down opponents health but more importantly nerfs their physical attacks which alongside intimidate allows Arcanine to sponge physical attacks with impunity, Morning Sun is the obligatory recovery move required of any defensive Pokemon (Just be mindful of the low PP and any weather that is not sun), and the last moveslot is a choice of your own preferences. Toxic allows Arcanine to beat other defensive Pokemon that rely on their own recovery move and gives Arcanine a more reliable means a damaging other Fire types that wall Flamethrower and are immune to Will-O-Wisp's burns, Roar prevents opposing Pokemon from setting up stat boosts while simultaneously racking up entry hazard damage and a chance to spread the Will-O-Wisp burns all around, and Fire Spin adds additional residual damage while at the same time trapping the opponent and preventing them from switching to a better counter.
Just a Show Dog (Gimmicky Doubles Set)
Ability: Justified
Item: Leftovers/Life Orb
Nature: Jolly
EV's: HP: 4 Attack: 252 Speed: 252
Moves:
Flare Blitz/Fire Fang
Extreme Speed
Wild Charge/Close Combat
Morning Sun
I briefly touched upon this in the abilities section as a joke, but I might as well try a novelty set.
The idea is to use Arcanine in doubles alongside a faster Beat Up user (Dugtrio, Sneasel/Weavile, Ambipom, Whimsicott) and have them attack Arcanine. With a full team of healthy Pokemon, Arcanine's attack is boosted to its maximum allowing it to sweep almost anything that stands against it. Flare Blitz has the most power but the recoil can spell your doom if you don't anticipate properly, so Fire Fang is a weaker and safer alternative if you prefer. Extreme Speed is obligatory of course to beat out other priority users that would try and pick off a weakened Arcanine after a Beat Up and receiving recoil damage from its moves. Wild Charge handles Water types better but Close Combat takes out Rock types that otherwise resist the STAB and Extreme Speed (However the defense drops can come back to haunt you in terms of longevity). And finally Morning Sun helps Arcanine recover health lost from recoil, Beat Up, and opposing attacks, just be weary that if you use Close Combat on this moveset that Morning Sun will become less viable once your defenses become compromised.