Let's say that I have an Utvara Hellkite and 3 other dragons on the battlefield. Do I get a 6/6 Dragon for every Dragon that's attacking, or just one?
On the card it says you get a 6/6 dragon token whenever a dragon you control attacks.
112.3c Triggered abilities have a trigger condition and an effect. They are written as “[Trigger condition], [effect],” and include (and usually begin with) the word “when,” “whenever,” or “at.” Whenever the trigger event occurs, the ability is put on the stack the next time a player would receive priority and stays there until it’s countered, it resolves, or it otherwise leaves the stack. See rule 603, “Handling Triggered Abilities.”
So every time the trigger event occurs. But you can't activate abilities when attackers are being declared.
603.2a Because they aren’t cast or activated, triggered abilities can trigger even when it isn’t legal to cast spells and activate abilities. Effects that preclude abilities from being activated don’t affect them.
There are two types of abilities (that use the stack): activated abilities (which can also be loyalty abilities) and trigger abilities. Trigger abilities can trigger whenever; hence the word whenever/when.
603.2c An ability triggers only once each time its trigger event occurs. However, it can trigger repeatedly if one event contains multiple occurrences. Example: A permanent has an ability whose trigger condition reads, “Whenever a land is put into a graveyard from the battlefield, . . . .” If someone casts a spell that destroys all lands, the ability will trigger once for each land put into the graveyard during the spell’s resolution.
For every occurrence. Even if no one can react between those occurrences.
So you get as many dragons as you attack with.