Do any relics other than the Vault Hunter Relic boost Rare Item Chance?
With the preorder bonus I got the Vault Hunter Relic which gives +5% rare item chance. The problem with that is I have never and will never equip another relic unless it has a better rare item chance.
So far (1/3rd of the way into playthrough 2) I've never seen another relic with + rare item chance. Are there any others, or am I going to be wearing this one forever?
Solution 1:
Vault Hunter Relic is the only relic that improves rare item chance.
In Borderlands 2 you can find Basic and Legendary relics.
Basic Relics
Vitality: Increases health stats.
Stockpile: Increases your ammo storage for different types of ammo.
Protection: Improves shield capabilities and damage absorption.
Strength: Improves melee abilities.
Resistance: Limits damage you take from different types of weapons.
Tenacity: Intensifies Second Wind abilities.
Proficiency: Decreases the action skill cool down rate.
Elemental: Provides an increase to elemental weapon damage.
Aggression: Provides a boost to a particular weapon type.
Allegiance: Reserved manufacturers products improved.
Legendary Relics
Lucrative Opportunity It causes shop timers to count down faster.
Deputy’s Badge It increases “Fight For Your Life Time” by 10% for every player who has this relic equipped. Location: Showdown
Sheriff’s Badge It increases “Fight For Your Life Time” by 15% for every player who has this relic on them. However, it is very rare and so more difficult to find. Location: Sheriff (Lynchwood)
Moxxi’s Endowment It increases the amount of XP earned by killing enemies but is rare. Location: The Good The Bad And The Mordicai Mission, Moxxi’s Endowment
Vault Hunter It enhances the probability of enemy dropping rare loot. It is also rare.
The Afterburner It intensifies vehicle boost capabilities and it is rare too. Location: Positive Self-Image
Solution 2:
The above answer by ChrisHatez covered the varieties of relic pretty well but it's also worth noting that the Vault Hunter's Relic is far less useful than it appears. It doesn't actually increase the drop rate of Purples, E-Tech or Orange weapons, only of greens and blues and even then, the increase is tiny. I made the same mistake as you, never unequipping it but you really are better off using something else given how little a difference it makes.
So I just investigated the Vault Hunter Relic data.
It modifies two attributes:
GD_Balance.Weighting.GearDrops_RareWeightModifier: +0.05 GD_Balance.Weighting.GearDrops_CommonWeightModifier: -0.06
Let's set them to +100.00 and -100.00!
Net result: I have not seen a single white weapon drop, greens drop, seen a few blues. Nothing else.
So, what I can gauge from this, is that it shifts a 5% of your chance for whites into non-whites. Doesn't touch anything else. Very low impact, perhaps bordering on useless.
Source: http://forums.somethingawful.com/showthread.php?threadid=3504490&pagenumber=133&perpage=40#post408051645 (page is now not viewable by unregistered users; same post quoted in the Gearbox forums)