Rarity

All collectible items have a certain Rarity associated with them. The more rare an item is, the better, but also the more difficult to acquire. There are five levels of rarity in the game.

Common
All low-level items are common-level. These items are white in color, and have no upgrades available. Disassembling them yields some glimmer but no materials. All common weapons do kinetic damage, except for Fusion Rifles. Common engrams will stop appearing at higher levels.

Acquired by: Purchasing from vendors, or picking up encoded engrams.

Uncommon
The next level is uncommon, which are green in color. Uncommon items have a few upgrades available, which cost some glimmer. Disassembling an item will yield a single upgrade material. Some special and heavy weapons will have an elemental damage modifier. Uncommon items cap off at level 18.

Acquired by: Purchasing from vendors, or picking up encrypted engrams.

Rare
Rare items start appearing at higher levels. Rare items have many upgrades available, though some will require upgrade materials as well as glimmer. Disassembling an item will yield two or three upgrade materials. All special and heavy weapons will have an elemental damage modifier (as do all special and heavy weapons in the above tiers). Rare items are still usable to a degree at higher levels, but are typically outperformed by legendary items.

Acquired by: Purchasing from certain vendors, picking up decoherent engrams, reward for strikes.

Legendary
Legendary items are more difficult to acquire. They have the most upgrades but also require ascendant materials to fully upgrade, making them quite expensive. Disassembling an item will yield upgrade materials as well as ascendant materials. In addition, Legendary items acquired in Raids tend to perform better than ordinary legendary items, whether its extra upgrades for weapons or higher light levels for armor. A few primary weapons will also have elemental modifiers.

Acquired by: Purchasing from faction vendors (requires reputation and special currency), picking up legendary engrams (very rarely drop), reward for Nightfall strikes and raids.

Exotic
Exotic is the highest tier of items available. Every exotic piece of equipment has a unique ability that sets itself apart from every other item in the game. However, only one exotic weapon and one exotic armor can ever be equipped at any time. Furthermore, to fully upgrade an exotic item, an exotic shard is needed, which has to be purchased or acquired from disassembling another exotic item.

Aquired by: Purchasing from Xur with Strange Coins, purchasing an Exotic Engram from Xur with Mote of Light, reward for Nightfall strikes and raids, completing an Exotic weapon bounty.