You will find a full list of all achievement rewards at Valve's Team Fortress 2 Wiki. Some are dependant on character milestones, while others rely on events that may be locked out. Several come as rewards for unlocking achievements in other games, on Steam.

Character Milestones

Character milestone rewards are unlocked for completing a certain amount of achievements in the respective class achievement category. I have included a link to each achievement list in the class name.

The Scout

• Force-A-Nature (rewarded for 10 class achievements)
• Sandman (rewarded for 16 class achievements)
• Bonk! Atomic Punch (rewarded for 22 class achievements)

The Soldier

• Equalizer (rewarded for 5 class achievements)
• Direct Hit (rewarded for 11 class achievements)
• Buff Banner (rewarded for 17 class achievements)

The Pyro

• Flare Gun (rewarded for 10 class achievements)
• Backburner (rewarded for 16 class achievements)
• Axtinguisher (rewarded for 22 class achievements)

The Demoman

• Chargin' Targe (rewarded for 5 class achievements)
• Eyelander (rewarded for 11 class achievements)
• Scottish Resistance (rewarded for 17 class achievements)

The Heavy

• Sandvich (rewarded for 10 class achievements)
• Natascha (rewarded for 16 class achievements)
• Killing Gloves of Boxing (rewarded for 22 class achievements)

The Engineer

• Frontier Justice (rewarded for 5 class achievements)
• Gunslinger (rewarded for 11 class achievements)
• Wrangler (rewarded for 17 class achievements)

The Medic

• Blutsauger (rewarded for 10 class achievements)
• Kritzkrieg (rewarded for 16 class achievements)
• Ubersaw (rewarded for 22 class achievements)

The Sniper

• Hunstman (rewarded for 5 class achievements)
• Jarate (rewarded for 11 class achievements)
• Razorback (rewarded for 17 class achievements)

The Spy

• Ambassador (rewarded for 5 class achievements)
• Cloak and Dagger (rewarded for 11 class achievements)
• Dead Ringer (rewarded for 17 class achievements)

Halloween Rewards

Halloween Rewards unlock by completing certain achievements within the Halloween maps and events. Most are more accessible during Halloween, but can still be unlocked throughout the year. Simply join a server running the appropriate maps.

• Necro Smasher (rewarded for Carnival Of Carnage: Step Right Up : *"Earn 4 of the Carnival of Carnage achievements)
• Halloween Gift Cauldron (rewarded for Carnival Of Carnage: Bumper To Bumper To Bumper : "Win each of the bumper car games in the Carnival of Carnage")
• Ghostly Gibus (rewarded for Ghastly Gibus Grab : "Dominate a player wearing the Ghastly Gibus")
• Ghastly Gibus (no longer available; rewarded instead of the "Ghostly Gibus" until 2012)
• Mildly Disturbing Halloween Mask (rewarded for Candy Coroner : "Collecting 20 Halloween pumpkins from dead players")
• Horseless Headless Horsemann's Head (rewarded for Sleep Holl0WND : "Kill the Horseless Headless Horsemann")
• MONOCULUS! (rewarded for Optical Defusion : "Kill MONOCULUS")
• Skull Island Topper (rewarded for A Lovely Vacation Spot : "Get to Skull Island".
• Bombinomicon (rewarded for Dive Into A Good Book : "Get to Loot Island")
• Unfilled Fancy Spellbook (rewarded for Hat Out Of Hell : "Get the loot from Skull Island in Hell"; Upgraded with Spellbook Pages to create Fancy Spellbook)
• Haunted Metal Scrap (crafting material, rewarded for Gored! : "Land a killing blow on the Horseless Headless Horsemann, while staying alive throughout the fight")
• Spellbook Page (crafting material, rewarded for The Mann-tastic Four : "Earn 4 Helltower achievements")

Content Update Achievements

These achievements relate to content updates and various other additions to the game.

• Full Head Of Steam (rewarded for Foundry Milestone : "Foundry pack achievements")
• Gentle Munitionne of Leisure (rewarded for Doomsday Milestone : "7 Doomsday pack achievements")
• Power Up Canteen (rewarded for Steel Fragnolias : "Complete all waves successfully in a Mann vs. Machine mission")
• Pyrovision Goggles (rewarded for A Fresh Pair of Eyes : "Kill a player wearing the Pyrovision Goggles")
• Director's Vision ( rewarded for Star Of My Own Show : "Spend some time editing a replay")
• Frontline Field Recorder (rewarded for Local Cinema Star : "Achieve 1,000 YouTube views for a Team Fortress 2 video")

Game Crossovers

These items are earned through alternate Steam titles.

Alien Swarm

• Alien Swarm Parasite (earned by completing Hat Trick : "Complete any two missions, on any difficulty level")

Alliance of Valiant Arms

• Black Rose (earned by completing 1st One Down : "Complete your first game")

CrimeCraft GangWars

• Bolt Action Blitzer (earned by completing Key to the City : "Achieve level 6")

Poker Night at the Inventory

• Iron Curtain (earned by completing Special Item: The Heavy : "Knock out The Heavy adfter he has brought in his special item.")
• Enthusiast's Timepiece (earned by completing Special Item: Tycho : "Knock out Tycho after he has brought in his special weapon.")
• Dangeresque, Too? (earned by completing Special Item: Strong Bad : "Knock out Strong Bad after he has brought in his special weapon.")
• Lugermorph (earned by completing Special Item: Max : "Knock out Max after he has brought in his special weapon.")
• License to Maim (earned by completing Special Item: Max : "Knock out Max after he has brought in his special weapon.")

Poker Night 2

• Long Fall Loafers (earned by completing Personality Goes a Long Way : "Win GLaDOS' bounty item.")
• Necronomicrown (earned by completing Book 'Em : "Win Ash's bounty item.")
• Samson Skewer (earned by completing Orb 'n' Legends : "Win Brock's bounty item.")
• Bloodhound (earned by completing Banjo Hero : "Win Sam's bounty item")
• Dapper Disguise (earned by completing Trophy Wife : "Win Claptrap's bounty item")

SpaceChem

• Moustachium Bar (crafting material, earned by completing the Moustachium levels)
• Spacemetal Scrap (crafting material, earned by completing Director of Moustache Research : "Beat the Assignment 'Moustachium 608'")
• 'Fish' (crafting material, earned by completing Moustache Scientist : "Beat the Assignment 'Moustachium 604'")
• SpaceChem Pin (earned by crafting 3 Moustachium Bars with a Spacemetal Scrap)
• Fishcake (earned by crafting 3 Moustachium Bars with a 'Fish')

Spiral Knights

• Spiral Sallet (earned by completing Mission Accomplished : "Reach the first Clockworks Terminal")

Super Monday Night Combat

• Flamingo Kid (earned by completing Rookie Agent : "Achieve agent level 5")
• Triclops (earned by completing All-Star Agent : "Achieve agent level 20")