You'll see people running, walking, cycling at all hours. Even when just walking I didn't carry valuables I was afraid of losing, but still enjoyed being there. There are signs painted to indicate where pedestrians vs. cyclists should go. There are lots of organized groups, inclduing the running and beer drinking Hash House Harriers, one of many such groups worldwide, which run (or walk, if you prefer) in various areas:
http://www.riohhh.com/