In Maricopa County, each city has discretion to operate a system of circulators or shuttles. Many of them do. Many of them are fare-free.
For example, in Scottsdale there are old-timey "trolleys" which look like streetcars, but they are just buses with fancy chassis. They operate routes which go through some neighborhoods and commercial districts, such as Old Town, to get people shopping and gambling and attending events.
In Tempe, there are "Orbit" buses which mostly drive through residential neighborhoods. They are mostly designed to get riders to-and-from standard bus routes and stations. You can also do plenty of shopping and sightseeing and day-drinking on these routes.
In Downtown Phoenix there is a system of "DASH" buses which, among other things, have serviced the Capitol area, which is due west of the downtown hub, where buses fear to tread, because it is also the site of "The Zone" where the worst street people congregate and camp-out.
Now all of these free circulators tend to be popular with the homeless, the poor, and freeloaders, but they are also appreciated by students and ordinary transit passengers, because we need to walk far less, and there are far more possibilities to connect from one route to another.
An innovative feature of many circulators is the "flag stop zone". Rather than having appointed stops with shelters, signs or benches, you can signal the operator that you wish to board or disembark, anywhere in the zone. The operator will stop where it's safe. While it is still a fixed route, it gains some of the flexibility for the passengers to make the most convenient stops.