I don't ask algorithm questions, and I wouldn't even dream of asking brain teasers. I ask questions like "Here's a pile of text that claims to be CSV, let's explore how you'd generate an HTML report out of it", and branch out from there depending on how the interview goes. I've got all sorts of directions I can go from there, from screwing up the input in various real-world ways, discussing HTML security and injection attacks, algorithmic complexity of the report, how to build a service out of this, how we're going to handle reporting errors, there's just an endless number of ways you can take the interview from there.
CS 201 doesn't usually come up.
The ideal would be pair programming for an afternoon.
Even if their "solution" is incomplete I look at if they get the gist right.