There is a lot of talk about the reason Confederate soldiers fought for. What was the story for the other side?
This is an interesting question. Often times, the Civil War is presented as a dichotomy of Confederates wanting to fight to maintain slavery and Union soldiers wanting to free slaves, but that's not entirely accurate.
New England was touched most heavily by the Second Great Awakening, and citizens of that region were imbued with much religious fervor. Abolitionism was strong in this region as well due to social reforms growing out of the Second Great Awakening. Slavery was seen as sinful. Many of the Union soldiers from New England joined to free slaves.
Also, remember, in 1848 and leading up to the American Civil War, revolutions broke out all over Europe. Many immigrants to the U.S. joined both Northern and Southern ranks because they wanted to be apart of cementing a new regime. The revolutions of 1848 did not bring about lasting change, but the American Civil War could.
Also, remember that racism was alive and well in the North, to the extent that Ohio, for example, opposed the admission of slave states nearby to keep fugitive slaves and freemen out. Those soldiers not from New England did not fight to free slaves, but fought to preserve the Union.
Others joined because a steady paycheck as a solider was better than life on the frontier. Some joined to travel. You have to remember that a lot of people didn't travel far beyond from where they were born. Further, some even joined to impress a woman.
Some were motivated to join out of a sense of community pride. Companies were formed in cities and town all over country. These companies would then be attached to regiments. Initially, the first 1000 men from Pennsylvania would be the 1st Pennsylvania Infantry, made up of ten companies from across the state. Oftentimes, a company would be organized by someone with clout in a community. If your brother, uncle, cousin, or neighbor joined, you would be compelled to join as well, to save face. Someone who refused to serve would be seen as a coward. Further, the idea was that if your friend or family was standing next to you, you'd be much less likely to run.
Individuals had lots of motivations for serving, and it varied from person to person
I'd like to add a historiograpic rider to this question and ask how historical perceptions of Union soldiers' motivations have changed over time.