Great responses. For me it's having a hobby that not only engrosses me to the point of boring the crap out of anyone who will listen, but keeps me home and occupied. I love the planning process; taking stock of what I have, do I have enough $$ to get what I need, and what I can do with it. My brewing journal entries can be 5 pages long before I even get to the brewday, what with planning, talking myself into or out of ideas, random thoughts, and tweaking recipes. Once it's finally brewday, I leap out of bed like a kid at Christmas and get to it. And it's my "me" time. I have two jobs, three if you count helping out at a local brewpub, and my brewdays are precious to me. I'm lucky enough to have a professional brewer as my mentor, who has taught me a lot of what I know, and is humble enough to listen to my ideas and expand on them. Not to mention cleaning out his shed and unloading his old homebrewing equipment on me so I could improve my own process.
But let's get to the REAL reason why most of us do this; we just love beer. Maybe not all styles, but for those of us who grew up in the 60's and 70's when there wasn't much out there other than light lagers and skunked imports, the plethora of recipes available to us now is fairly mind-boggling. I've loved the taste of beer as long as I can remember, as a little girl of four years who was proud to bring Dad a beer, and got a sip; by the time I was six I could have about 1/2 inch in a glass for myself. At 14 I was allowed to have a can to myself (took me over an hour to finish, and then slept a LONG time). As a result I wasn't one of the kids in school who stole Dad's beer to get drunk; I could have one when I wanted, and even today I don't like to get drunk for the sake of getting drunk, just love the taste of that beautiful fizzy deliciousness in my glass. Making my own has taught me more chemistry and math than I ever learned in school, and brought me satisfaction that no other hobby in my life has even come close to.
And I hope some of the noobs get to this part of this long rambling post; yes you're going to have failures, and mishaps, and feel like throwing your mash paddle through the window; all of us have. But to me there is no better feeling in the world like pulling the first glass of a perfectly carbed whatever I've brewed, tasting it, loving it, and proudly saying to myself, "I brewed this. It's really good. I'm damn proud of myself."
Brew what you like. Like what you brew. And always, ALWAYS, be constantly open to learning.