Does your favorite author have a website? More often than not, the answer is yes. Authors spend a lot of time working alone, in quiet rooms, so they often welcome the opportunity to connect with their readers in a casual way. A website gives them a chance to keep their fanbase informed of upcoming releases, and publicize titles of earlier works they may know about. Also it can be one more creative outlet, or outlet for wackiness, like Dave Pilkey's Extra Crunchy Website o' Fun. (Dave is the author of the Captain Underpants books.)
Some author websites have a lot of the author's style in them, like jkrowling.com, author of the Harry Potter series. Not surprisingly, it's a pretty slick website. For something a little more homey, check out murdershebaked.com, the home of Joanne Fluke, author of the Hannah Swensen mystery series, whose titles include The Cherry Cheesecake Murder, The Key Lime Pie Murder--you can see where this is going. There are recipes in each book, and more recipes on the website. (I haven't read any of the books, but I can recommend the recipe for the Black Forest Brownies in The Carrot Cake Murder.) Prolific writer noraroberts.com falls somewhere between the two, and features freebies (send a SASE to get a free magnet) as well as links to interviews, a message board, etc.
If a book started as a blog, as many do these days, the website can contain additional material that didn't make it into the book. The Julie/Julia Project was the blog that became the best-selling book Julie and Julia : 365 days, 524 recipes, 1 tiny apartment kitchen : how one girl risked her marriage, her job, and her sanity to master the art of living, by Julie Powell, and then a movie, Julie and Julia, starring Meryl Streep in Oscar-worthy form. (Yes, I still think she should have won.) The blog's still up, with the comments removed. Other blogs remain active after the publication of their companion book, including The Happiness Project, by Gretchen Rubin, and No-Impact Man, by Colin Beavan. The thriller and mystery writer J.K. Konrath has a site that features a lot of useful insights into self-publishing. I would read more of his books but I'm waiting til the nightmares I got from Afraid stop. How he can be so funny, and write such scary stuff, I dunno.