Movement

Speed

Speed is measured using hammer units / sec. The standard is 300 hu/sec, or 100%. This is the speed of the Pyro, Sniper, Engineer, and Spy. Note that speed while moving backwards is 90% of what it would be otherwise, and while crouched it becomes 33%

Scout

Default: 133%

Baby Face's Blaster, uncharged: 87%

Baby Face's Blaster, charged: 172%

With Crit-A-Cola effect: 167%

Soldier

Default: 80%

Escape Plan, 121-160 Health: 88%

Escape Plan, 81-120 Health: 96%

Escape Plan, 41-80 Health: 112%

Escape Plan, under 40 Health: 128%

Pyro

Default: 100%

With Gas Jockey's Gear set: 110%

Demoman

Default: 93%

With Head-Taking Sword equipped and 1 head: 101%

With Head-Taking Sword equipped and 2 heads: 108%

With Head-Taking Sword equipped and 3 heads: 116%

With Head-Taking Sword equipped and 4+ heads: 123%

With Scotsman's Skullcutter equiped: 73%

Charging with Chargin' Targe or Splendid Screen: 250%

Heavy

Default: 77%

While Minigun is spun up: 37%

While Brass Beast is spun up: 15%

Wielding Gloves of Running Urgently: 100%

Engineer

Default: 100%

While hauling a building: 75%

Medic

Default: 107%

Wielding Overdose at 100% charge: 117%

Healing a Scout with Quick-Fix: 133%

Sniper

Default: 100%'

With a Rifle zoomed in: 27%

With Huntsman drawn: 53%

Spy

Default: 100%

Disguised as Scout: 100%

Disguised as Heavy: 77%

Disguised as Soldier: 80%

Disguised as Demoman: 93%

Other Movement Techniques

Double Jump

When in the air as scout, Scouts can press jump again for an additional jump. This can go in any direction, and is extremely useful for maneuvering around maps or throwing off attacking opponents.

Rocket Jump

Main article: Rocket Jumping

Soldiers can jump, crouch, and shoot a rocket near themselves to go flying through the air. This can be useful for running towards a battle, obtaining height advantage, or fleeing to safety. Gunboats causes Soldiers to take 60% less damage while rocket jumping.

Sticky Jump

Main article: Sticky Jumping

Demomen can also jump, crouch, and detonate a sticky near their feet for a boost. This causes more self-damage than a Soldier's rocket jump, but also provides a bigger boost. A Demoman will almost always sticky jump during the rollout at the start of a round.

Explosive Surfing

Any class is capable of timing a jump with an enemy's projectile and using it to their advantage. This is a common practice among Medics, who often surf away from damage and to the safety of their team.

One particular example of this: http://youtu.be/2IcWmpkjMKo?t=4m5s