It is perhaps foolhardy to talk about teaching in a post immediately following one in which I bemoan my teaching failures, because I may be inviting people to connect the two ("well, of COURSE her teaching went badly at Former College if THAT's what she does in class!"), but teaching is on my mind at the moment, so...
My MW class this term gets, well, a little distracted sometimes (this student is a prime offender, actually). We get off topic. But you know, there are things I like about this: it comes about because the students ask questions, questions inspired by the topic at hand. Sure, the questions aren't always relevant to the topic at hand (in fact, they're often not), but they're triggered by it. And I like it that what we're talking about makes them think of something, even if sometimes the connection is kind of out there. Because they're engaged enough to think, and it's neat to see them connect what's happening in our class with what they know from other contexts.
(Want an example? Someone today asked if something we were talking about today was so, then why was it such a big deal when Henry VIII wanted a divorce? It was kind of a cool question, which you'd probably be able to appreciate better if I wasn't being purposely vague about what we were actually talking about today, which has nothing at all to do with Henry VIII, being four hundred years and a continent away from the guy.)
The other reason I like it: when students ask these veering-somewhat-off-topic questions, the other students respond to them. They start talking to each other. It's like if we're not strictly on the exact topic of the course, they feel like they can be authorities, too, and they don't have to wait for me to answer. I don't want the students to (and don't let them) spread misinformation, but it's fun to see them start conversations of their own about the subject (or at least something kind of vaguely related).
Obviously chaos has its down sides, too. Uncontrolled chaos is a problem, and controlled chaos can easily devolve into the uncontrolled variety. There's only so far you want to let distractions go. For instance, after the Henry VIII question, another student said, "Henry VIII? He chopped the heads off his wives, right?" Which comment inspired other students to start explaining everything they knew about Henry VIII (no, that was not allowed to continue). And the danger with students' own conversations is that they can move entirely away from the course topic (or anything academic), and it can be hard to bring them to a close gracefully when you want to.
And what you really don't want is for the digressions to get self-indulgent - where I and some students are happily chatting away about topic x (even when it is connected to the course material), and folks in the back row who aren't part of the conversation are getting bored. This is where controlling the chaos is necessary, so there can be room for these deviations and expressions of student interest, at the same time that you don't lose anyone through boredom or simple confusion about what does this have to do with the course, again?
It can be an interesting balancing act sometimes, and sometimes pulling them back from the brink is takes a little effort. Usually pointing out explicitly that while interesting, these questions don't really connect to what we're doing and we need to get back to the course material, is sufficient. Making sure to catch everyone's eye to bring their attention back to the room as a whole can work, too (depending on how big your class/room is). I do find myself often raising my voice, trying to talk over their conversations, but I don't think this is usually very effective - they just talk louder too, which intensifies the sense of uncontrolled chaos. I have a friend who, in such situations, starts to talk really quietly (and when they finally calm down to be able to hear her, she says, "And what I just said will all be on the test." Hee!), and I have to remember to try that. I'm more likely just to stop talking, and stand and stare at them till they realize, wait, isn't that person in the middle of the room supposed to be doing something?
Different classes also have very different propensities for chaos, too. Some are quiet, and docile, and others are rowdy and ready to change paths and the slightest provocation.
So, what about you? How much chaos do you feel comfortable with in your classroom, and how do you control it?