I discovered his books post WoT, no more than half a year ago actually. However, WoT had nothing to do with me reading his books, because I had never read those either. In fact, I really hadn't read any books yet. I had read the obligatory Harry Potter and Lord of the Rings books throughout high school, but was never really a book person. About a half year ago I found my self craving some good fantasy stories, but having exhausted all lines of movies and TV series that I cared to watch, I figured I'd give some books a try. I started searching Google for websites that reviewed fantasy novels, and the first book that really stood out to me was tWoK.
What really grabbed my attention in the descriptions of tWoK was the interesting world with odd fauna, strange animals, and a totally unique world ravaged by highstorms (the book cover was also very intriguing, which I later found out through research was actually quite a big deal to BS, since a book cover was what originally helped him choose his first book to read in school.) I started reading it and was just blown away. I couldn't stop reading it, and it quickly became to me, the best story I had ever experienced, films included.
Because only the first book of the series had been made, I quickly looked up other novels written by BS to hold me over until the second came out. I moved on to Mistborn which yet again, blew me away. Since then, I've finished the Mistborn series (including Alloy of Law,) Elantris, am part way through Warbreaker, and have also made by foray out into books by other authors. I pretty much cling to BS's twitter feed hoping for new tidbits of information and news of the second book of the Stormlight series, which continues to be the best book I have read to date.
So I guess you could say Brandon Sanderson is the reason I became a reader. I hope he comes to the DFW area of Texas some day so I can meet him in person to thank him, and maybe get some books signed.