Trinkets are boss rewards, so you can't force the exact one you want — but when these show up, they're almost always worth taking:
Trinkets are boss-reward items. Act Bosses between rounds drop them, and each Trinket bestows a unique effect on whichever Dude equips it — most effects are keyed to the Wielder, so pairing the right Trinket with the right Dude is where the build-crafting depth comes in:
Looking for a specific effect? The full official list below is searchable.

ADHD
Boosts the Wielder's Run Speed by 40%, and every 4 seconds he Dashes straight at the enemy farthest away from him.

Airhorn
Each second grants the Wielder 5% Attack Power and 5% Run Speed that persist for the whole battle, with up to 10 stacks.

Bad Credit
Half of incoming damage is Stored and spread across 4 seconds, with a 50% chance each second to Expel 50% of it as Direct Damage on the Best Fit enemy.

Bag of Nuts
There's a 5% chance the Wielder goes nuts while dealing Direct Damage, granting him 50% Attack Speed for 2 seconds.

Baseball Bat
Once every 3 seconds the Wielder swings at the nearest 4 enemies, hitting each with Direct Damage worth 25% of his DPS, and every hit always Crits.

Black Belt
Adds 10% Evasion, and whenever an Evade happens there's a 20% chance to counter with Direct Damage equal to 100% of his DPS.

Bongos
Each second flips the Wielder between a 20% Evasion boost and a 20% Deflection boost.

Crazy Straw
Grants 10% Lifesteal; every time he Lifesteals he picks up 5% Crit Chance lasting 3 seconds, stackable up to 2 times.

Cutoff Jorts
Every 25 feet of travel nets the Wielder a stacking 1% Attack Power that holds for the remainder of the battle.

Diss Track
Copies 30% of the damage all its Wielders dish out, holding it in Storage; each second that Stored damage is Expelled onto the Best Fit enemy.

Ear Gauges
Upon taking Fatal Damage the Wielder Heals to full and gets 30% Attack Power for the rest of the battle, on a once-per-battle Cooldown.

Face Tattoo
Grants 10% Deflection and reroutes all Deflected Damage to the Wielder, who gains 5% Toughness for 4 seconds whenever he takes it, up to 5 stacks.

Fedora
Scales 3% Attack Power and 1% Max HP by the gap between the Roster's most common Dude Type count and the Wielder's own Dude Type.

Folding Chair
Dealing Attack Damage gives a 20% chance for a follow-up strike that lands Direct Damage equal to 30% of the Wielder's Max HP.

Friendship Bracelet
Survives Fatal Damage by Equalizing HP with the Dude holding the most HP, an effect that runs on a 2 second Cooldown.

Ghillie Suit
Adds 10% Crit Chance and 15% Attack Power, and makes the Wielder completely immune to being Cleaved.

Glass Cannon
Each Critical Hit lands the Wielder a stacking 5% Attack Power plus 1% Vulnerability that both last the rest of the battle.

Inhaler
Any heal the Wielder performs has a chance matching his Crit Chance to also Heal the most-injured Roster Dude by the same amount.

Laser Pointer
Every second, each Wielder has a 20% chance to teleport a random Dude of the Dude Type below him to a random distant Dude or enemy and grant him 20% Attack Speed for 2 seconds, stacking up to 3 times.

Medical License
For each 100 damage dealt, the Wielder Heals some random injured Roster Dude for 15.

Neckbrace
Raises Max HP by 20%; if damage pushes him under 30% HP he gains Temporary Health worth 50% of his Max HP for 4 seconds, on a 4 second Cooldown.

Pet Rock
Adds 10% Block Chance; each successful Block earns 10% Crit Chance and 20% Crit Damage for 2 seconds.

Receipts
A Direct Crit carries a 50% chance to Taunt 2 nearby enemies while granting 10% Toughness and 5% Lifesteal for 4 seconds, stacking up to 2 times.

Rizz
Roster Dudes sitting next to the Wielder receive 1% Crit Chance and 1% Evasion per 2 Wielders, stacking up to 10 times.

Scrubs
Provides 20% Deflection, and every Deflect carries a 20% chance to grant 30% Attack Power for 2 seconds.

Shiv
Attack Damage triggers a follow-up strike with odds matching the target's missing HP Percentage, dealing Direct Damage equal to 60% of Attack Power.

Shovel
For each Unconscious Dude on your Team, the Wielder picks up a stacking 20% Cleave for the battle.

Socialism
Every 2 seconds a random injured Roster Dude gets Temporary Health equal to 25% of the Wielder's Max HP for 3 seconds.

Taser
Each 50 feet of movement makes the Wielder zap a nearby enemy for 50% of his DPS.

Team Jersey
During battle, the Wielder gains 10% Attack Power and 3% Deflection for each nearby Dude of the same Dude Type, stacking up to 4 times.

Therapy
Above 70% HP the Wielder enjoys 30% Toughness, which tapers down to 10% Toughness as his HP nears 20%.

Weighted Vest
The Wielder trades away 50% Run Speed in exchange for 30% Toughness and 30% Attack Power.