I was a vegetarian for several years, though never really considered veganism seriously; I mostly cut out meat and milk for health reasons (to avoid the chemicals and hormones injected in meats and milk), though was unwilling to eliminate cheese, ice cream, eggs, butter, or the occasional fish. I never saw it as an issue to consume these things - animals weren't being killed, right?
When I came back to vegetarianism in the summer of 2012 (and Ian joined me), my reasons were very different; I did not feel it was ethically right to kill animals for consumption, and wanted to avoid participating in how the meat industry is contributing to global warming. It only took a couple of weeks before I realized that cutting out meat was not enough; after doing some research and better understanding the horrific things animals are put through to get dairy products, for instance, we decided to become vegans.
As we've continued in our vegan journey, our convictions have only grown. Initially I wasn't so much against animals being killed as long as they were raised humanely, and killed humanely, but now I believe that any killing for human consumption is wrong (with the exception of bivalves, which have no nervous systems, thus cannot feel pain).
If you're wondering why someone would become a vegan, or even a vegetarian, I strongly encourage you to take some time to watch the video below featuring Gary Yourofsky. While I don't condone everything he does, he has many good examples and arguments for why veganism is important.