I do from time to time, usually if I’m in the middle of a good book and I gotta walk to class or something. My peripheral vision didn’t let me run into anyone or anything so it worked fine.
Ah… so I’m not the only weirdo. Thanks for the votes of confidence. I just don’t understand why people feel the need to interuppt me to comment on it… sigh…
I do “read” audiobooks in the car, but it’s not the same, and I’ve just about exhauseted the library’s selection.
I do this all the time, even in stairwells.
I did it all through middle school and high school. It’s funny, because when I run into people I went to high school with but didn’t know very well at the time, they often say things like 'You’re that girl who was reading all the time. You must be really smart!"
I have always done that.
I never go anywhere without a book and a spare book.
I must eiter be very lucky or totally oblivious, as I have never gotten ribbed adout it.
I have a 7 minute walk to my office from my apartment, which I make use of to read sometimes. The path I take is through the woods and not very crowded with other people. There’s only one street I have to cross, and I try to tear my eyes from my reading material long enough to cross the street safely.
When I was little I used to read in the car while my parents drove. They were always amazed I didn’t get carsick. I also used to read during recess, and even during class after I finished my work. (I went to a Montessori school, where we had free time if we finished our work early.)
Reading Harry Potter during an electromagnetism lecture in college probably crossed the line, though. (It was my friend’s fault–what was she thinking giving me the book right before class started?!) 
I read while I walk, too, and I get comments. I don’t care. I love reading and I basically spend all my free time reading, whether it be online or in print. The only time I’m not reading something is when I am not physically able to–at work (excepting breaks), on the telephone, in the car (I get carsick! It sucks!), etc.
And I’ve never had an accident of any sort while walking and reading, except a few times I’ve not noticed an uneven sidewalk (that I would have, otherwise) and taken a funny step. But I’ll live with that mild embarrassment.
I love knowledge, even if I don’t have an especially high IQ or fabulous career as a result.