I felt like I got very lucky with this one. I went to a career fair at my school, asked them about the Product Engineer position I had read about on Micron's job listing site, and there happened to be a Product Engineer there who went to my school. 2 days later, I had a phone interview with him (1 hour). It was almost all technical questions, from device physics (MOSFETS), to digital logic (3-input XOR gate), registers and latches, then an out-of-the-box puzzle that Micron loves to give. Went well, and the next day they told me they would bring me in for an on-site interview.
The on-site was long and difficult. Each member of the team I would be working with (6 people) interviewed me for 1 hour. They were all very nice and understanding, like helping me work my way to a solution if I didn't know it right away. They knew who I was by then, so it was pretty much all technical questions--statistics, CMOS logic, timing diagrams (digital systems), programming (C and Verilog), and again, a few mind-bending riddles which sort of relate to critical thinking and programming skills. After this interview, they made me an offer within 3 days and I accepted it a few days after that.