While I think that my reasons for going to conferences will to some extent remain the same, the primary reason that I love going to conferences as a graduate student is that I find them inspiring. I honestly come away from conferences positively high off of ideas. And that is what has made me a conference addict. I love the thrill of new ideas, of sharing ideas with other people working on similar projects, and really just expanding my intellectual horizons. Of course, one of the biggest thrills is learning about possibilities for projects that I had never thought of before or new ways of looking at a topic.
Going hand-in-hand with this is my need to ask questions. I'm generally not afraid to ask questions (or make a fool out of myself) and use conferences as an opportunity to ask experts and colleagues about research questions that are weighing on my mind. I've never been big on being star struck, but it does tickle my geeky soul to be able to talk directly to the historians who have written the books that I dearly love and have shaped my path as a historian. Writing up my questions of an author's work in a book review helps me to frame my interpretation of that person's book, but asking for feedback directly is so much more gratifying.
Yes, this does sometimes backfire. I've gotten a little over excited about grilling two different prominent southern historians (and I'm hoping that they forget both my name and face), but one of those instances resulted in me being asked to write an exhibit review for the JAH (word of advice, don't quote someone's book at him in the middle of a session...that's a little too sycophantic). Also, those occasions have made for great stories afterward (and what historian doesn't love a good story?). So my advice is don't be afraid to put yourself out there and take the opportunity to engage other scholars, ask questions, and explore new horizons.
It is also kind of amusing to be able to say in a seminar discussion after a conference, "Well, when I was talking to Cathy Stanton last week about this very topic, she said..." For historians who are already well established in the field, these kinds of conversations are normal. For grad students...well, I just think that it is cool.