Destiny's Exotic weapons are meant to rise above the rest of the crop, supplementing your arsenal of (ideally) legendary gear with elite ability and power. You can only have one equipped at any given time, however, and that gives you a decision to make about which weapons to carry into battle.
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Our rankings should help you pick out which Exotic weapons you want to aim for and use if you're not already well-versed in Destiny's arsenal. These are the top overall gold-tier weapons, ranked in order of their power in relation to PvE. This is based on Attack value, talents, and a bit of opinion--the last spot is likely up for debate. That said, and without further ado, I give you the top 5:
1. Gjallarhon
The rocket launcher that still evades most of the game's players, Gjallarhorn is simply the most powerful weapon in Destiny. If its Solar damage, high attack, and homing rockets weren't enough, Gjallarhorn's missiles split into smaller projectiles on impact, which also track enemies before exploding again. This effect basically equates to hitting an enemy with the damage of two rockets at once, and that's just not something any other weapon in the game can match. You can also draw, aim, or reload the weapon quickly depending on which talent you choose, and it happens to be adorned with awesome wolf carvings, to boot.
2. Ice Breaker
The exotic Sniper Rifle was finally sold by Xur recently, giving the community what it wanted. Ice Breaker's power is appealing in itself, with Solar damage and rounds that cause enemies to explode, but its real draw lies in the unique No Backpack talent. Ice Breaker can't be reloaded, and instead refills its own ammo every few seconds to a maximum of six bullets. This makes it extremely useful in Raids, even if the rate of fire is slow compared to other snipers and the shots have high recoil. Camping on the top ledge during the Templar and Oracle fights in Vault of Glass is much easier with infinite ammo (it's even difficult to pull the strategy off at all without Ice Breaker), and the gun is very useful for taking on Crota. In addition, Ice Breaker is generally useful in taking out enemies at any time and can help lock down parts of the map in the Crucible.
Perhaps the game's most unique weapon, the Mythoclast is classified as a Fusion Rifle but takes a Primary weapon slot. In reality it functions more like a high-impact Auto Rifle, and can only be attained as a drop from Atheon in the Vault of Glass Raid on Hard. It fires rapidly, deals Solar damage, and can be upgraded for greatly increased stability and power. It was the game's best weapon before The Dark Below, but was curiously not bumped up to the 331 Attack ceiling with other Exotics and sits at its own 323 rating. It's devastating against crowds (and in the Crucible), and has the added bonus of looking incredibly awesome.
4. Hawkmoon
The PlayStation-exclusive Hand Cannon (until Fall 2015) doesn't have many frills, but is fundamentally just a very strong weapon. Its impact rating is off the charts, and it has a larger than normal clip (13 bullets) for its weapon type. Hawkmoon's talents revolve around random bullets from the clip doing bonus damage, and that's about where the special features end. With its high attack, impact and ammo, however, it hardly needs bonuses to deal serious damage.
You can acquire this extremely well-balanced Auto Rifle in a variety of ways, including from Xur, engrams, and PvE or PvP rewards. It's a jack of all trades, and has a high impact, good rate of fire, and remains very accurate. Additionally, the bottom half of your magazine deals bonus damage, and has a chance to heal you when the shots land. It's not the flashiest weapon, but it gets the job done in a world of special talents and effects across a variety of game modes.