Question

Why did the United States decide to enter the war and fight on the side of the Allies?

Answer 1

In both World Wars I think for a mixture of traditional ties with England and because attacked or instigated to enter the war by offensive actions of one side (Germany and Japan).

Explanation:

United States of America always had strong connections with England. Although the Americans fought a bitter independence war against the British, England remained the country of origin...the place of cultural and traditional influence...a kind of distant motherland for many Americans and seen as a reference and inspiration (even the language was basically the same helping to understand better the issues and opinions).
But...

The USA, prior to the First World War, was also a place of immigration full of people that saw Europe as...a hellish place, full of violence (wars each few years), hunger, misery and pestilence and governed by tyrants and despots. So, it is not very strange that at the start the US population wasn't very enthusiastic to go to die for a place they escaped from!
Remember that there was also a big German immigrant’s community in the US not very inclined to fight against Germany!
The president himself (W. Wilson) was in a dilemma as well: US loans and investments were tied to Europe and to support one side meant loose the money of the other!

Germany solved the impasse sinking few "civilian" ships (SS Lusitania, for example) full of innocent American citizens and sending a message (the Zimmerman Message) to the Mexican government promising southern territories (Texas, Arizona, New Mexico) in exchange of an attack against the USA (message promptly discovered by the British and disclosed to the US government).

At the time of WWII the situation was quite similar. This time the Americans didn’t like the idea of being dragged again in a bloody war in Europe having witnessed directly the horrors of the previous one. Roosevelt was maybe inclined to enter the war to help England (and gain, if victorious, a prominent place in the World’s political scenario that once belonged to England) but again it was necessary the attack on Pearl Harbor to push the public opinion towards it!