Guide to Obtaining Shouts [updated 11.25.11]
Our hero is the Dragonborn, which means he can shout in the language of dragons. These shouts are not as powerful as magic, and the cooldown for a single shout is such that you can kill any enemy in that time, but when used appropriately, it can dramatically turn the fight in your favor. This guide classifies all the shouts, their power, cooldown, etc.
A Brief Overview of Shouts:
You receive your first shout almost at the beginning of the story, after killing a dragon (a main quest, everyone who has played Skyrim for more than an hour and a half has encountered it). For now, this shout is weak and unupgraded, it won't help you (and won't change the game at all), and to receive the next shouts you need to visit the Greybeards. Each shout can consist of one, two, or three words respectively, each word is unique and has its own meaning, but for simplicity, we will categorize shouts into first, second, and third levels (seriously, is anyone interested in a dragon-Russian dictionary here?). The higher the level, the longer the cooldown will be, and to activate the shout, a dragon soul will be required.

So that it goes like this
Ruthless Force
Effect: a shove that pushes and disorients the enemy.
Application: direction towards
Cooldown: 1st level – 15, 2nd level – 20, 3rd level – 45.
Where to find: during the main quest (2 words), "Whiterun Peak" (3rd)
Fear
Effect: causes enemies to flee from you at full speed
Application: all space around
Cooldown: 1st level – 40, 2nd level – 45, 3rd level – 50.
Where to find: in the Labyrinthian (Winterhold College quest)
Swift Dash
Effect: the hero covers a short distance in a matter of milliseconds
Application: direction towards
Cooldown: 1st level – 20, 2nd level – 25, 3rd level – 35.
Where to find: with the Greybeards, in the Resting Place and in Volskygge
Intangibility
Effect: for a short time, you cannot be attacked (and you can't attack either)
Application: on yourself
Cooldown: 1st level – 20, 2nd level – 30, 3rd level – 40.
Where to find: Ustengrav (according to the Greybeards quest)
Elemental Fury
Effect: a temporary increase in attack speed
Application: on yourself
Cooldown: 1st level – 30, 2nd level – 40, 3rd level – 50.
Where to find: "Northern Bastion of the Howling Wind" (north of Falkreath), Dragontooth Crater
Clear Skies
Effect: control of the weather
Application: direction towards
Cooldown: 1st level – 5, 2nd level – 10, 3rd level – 15.
Where to find: during the main quest
Fire Breath
Effect: guess what
Application: direction towards
Cooldown: 1st level – 30, 2nd level – 50, 3rd level – 100.
Where to find: during the main quest, "Resting Place" (here), Dustman's Cairn (south-southeast of Labyrinthian), Sunderstone Gorge (west of Riverwood)

Dragonrend
Effect: forces a dragon to land
Application: direction towards
Cooldown: 1st level – 10, 2nd level – 12, 3rd level – 15.
Where to find: during the main quest
Call Dragon
Effect: summons a dragon to assist you (until all enemies are dead)
Application: on yourself
Cooldown: 1st level – 5, 2nd level – 5, 3rd level – 300
Where to find: during the main quest
Time Slow
Effect: slows down time -_-
Application: all space around
Cooldown: 1st level – 30, 2nd level – 45, 3rd level – 60.
Where to find: Korvanjund cave (quest from the Brothers of Storm/Imperials), in Labyrinthian (Winterhold College quest), Witch's Nest (west of Dragon Bridge)
Call of Valor
Effect: Sovngarde comes to help
Application: on yourself
Cooldown: 180 for all 3 levels
Where to find: during the main quest
Frost Breath
Effect: similar to fire breath but slows down enemies
Application: direction towards
Cooldown: 1st level – 30, 2nd level – 50, 3rd level – 100.
Where to find: "Altar of the Skyborn" (east of Morthal), Folgunthur cave (northeast of Solitude)
Animal Allegiance
Effect: animals come to your aid
Application: all space around
Cooldown: 1st level – 50, 2nd level – 60, 3rd level – 70.
Where to find: Angarvunde (somewhere near Riften), Ancient's Ascent (southwest of Riverwood), Ysgramor's Tomb (somewhere near Winterhold)

Aura Whisper
Effect: detection of enemies (?)
Application: all space around
Cooldown: 1st level – 30, 2nd level – 40, 3rd level – 50.
Where to find: Northwind Summit (northwest of Shore Stone)
Marked for Death
Effect: reduces the stamina of the enemy
Application: direction towards
Cooldown: 1st level – 20, 2nd level – 30, 3rd level – 40.
Where to find: "Autumn Watch Tower" (south of Ivarstead), "Forgotten Cave" (here), Dark Brotherhood hideout
Storm Call
Effect: heavenly lightning strikes your enemies (only outdoors)
Application: all space around
Cooldown: 1st level – 300, 2nd level – 480, 3rd level – 600.
Where to find: Forelhost (southeast of Riften), High Gate Ruins (east of Solitude), Skuldafn
Calm
Effect: enemies are no longer interested in you (only works on animals)
Application: direction towards
Cooldown: 1st level – 40, 2nd level – 50, 3rd level – 60.
Where to find: "Way of the Ancients" (here)
Voice Throw
Effect: a whisper that makes enemies seek you out
Application: all space around
Cooldown: 1st level – 30, 2nd level – 15, 3rd level – 5.
Where to find: "Two-Headed Peak" (near the Valtain towers) (all 3 words)
Ice Form
Effect: turns the enemy into an ice statue (yes, they don't move and fall to the ground)
Application: direction towards
Cooldown: 1st level – 60, 2nd level – 90, 3rd level – 120.
Where to find: Mount Antor (south of Winterhold), Saarthal (also near Winterhold), Ice Crypt southwest of Dawnstar
Disarm
Effect: disarms the enemy
Application: direction towards
Cooldown: 1st level – 30, 2nd level – 35, 3rd level – 40.
Where to find: "Peak of Ancients" (south of Morthal)
Of course, the list of locations is far from complete, but it will be updated. Please point out any mistakes in the comments and without swearing :) The locations of the shouts are the same.
And for dessert:
upd.
A complete English guide to shouts has appeared (and all my efforts went down the drain).
Link.
Just select the desired shout, click on the location, and follow. Soon I will try to supplement the article with information in Russian :)