During the Companions Quest The Silver Hand, you will encounter Aela in her lycanthropic form, and you should become a werewolf by drinking her blood.
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ADVANTAGES

You can feed on corpses instead of looting them.Wolves will not attack (They can come to your aid)Magicka is replaced by BloodlustAble to use shout-howls

While in werewolf form, these can happen:

Your inventory is inaccessible (Like Bloodmoon)Can only use unlocked doorsYou will be hated and feared by most npcs (Except for factions with named werewolves)You can't leave the form yourself (Not feeding on corpses causes your form to swap)

The Dawnguard DLC adds a werewolf perk tree. The skill has the name of the beast. The totem perks will give changes to Hircine's totems. Bestial Strength increases your damage and Animal Vigor will increase your health/stamina.

Werebears are added by Dragonborn, and you can't take on the werebear form.
Transforming in front of a guard is an easy way to get the Master Criminal achievement.
Shout-howls during full moons is often called "Howling at the moon" and it can only happen during a full moon.
Some hunters are infected with lycanthropy, but if you're in werewolf form while they are, they will still be passive.
The addon Werewolf Potion allows you to change your form via a potion.
Claws deal extra damage.