Interesting to see that most of the responses here are from North America.
As I've mentioned on other threads, numerous times; as others have mentioned here, in the UK (and much of Western Europe, from my experience) the trend is now towards removing them - or not replacing dividers, where they were originally installed.
In Victorian times, most UK urinals were waist high, elaborate enamel, concave shaped and floor draining - the concave shape virtually wrapped around your body from floor to waist. Then came basic troughs, with little modesty afforded.
In the 1970s, the now familiar wall-mounted 'pot' started to become popular ,when toilet blocks were refurbished, complete with solid, enamel dividers between them. However, the more anti-social members of society found that these were easy to smash (as, to be fair, were the 'pots') - especially during the era of football hooliganism, from the late-60s to mid-80s. Additionally, they require a lot of cleaning. Most toilet blocks (outside of places like airports), certainly in the UK, are unstaffed and only cleaned once or twice a day by travelling cleaners.
Over the last 20 years or so, any new installations and any refurbishments have tended towards wall-mounted urinals, with no dividers. Councils have found it cheaper (and probably more hygienic) to dispense with dividers entirely. As others have said, it's rare to find them now, except in blocks that were refurbished in the 1970s and haven't really been updated since.