A couple of my 286-based Toshiba portables (1986-1987) and IIRC one of my 386 Toshiba portables (~1987) only work with 720K floppies. Conversely, I have a WYSE 286 system (Exact age unknown, but assuming about the same age because of EGA graphics) that has both a 1.2MB 5.25in drive and 1.44MB 3.5in drive...although admittedly one or both of those could have been upgraded by the previous owner (I have no evidence suggesting they were upgraded, though).
I also have an Amstrad PPC640 from 1988 with dual 720KB floppy drives, but the only reason it uses 720KB floppies so late in the game is because it was designed to be as utterly inexpensive as possible.
I also remember in 1993 getting a then-new Smith Corona electronic word processor that only accepted DOS-formatted 720KB floppies (Although it did not run DOS), but again I imagine the desire to use the cheapest possible parts played a role here. Also, the fact that it's more of a specialty product as opposed to a general-purpose computer, so they could get by with using lower-end and older hardware.
My ~1986 AT&T PC 6300 has two 360KB 5.25in floppy drives, with AFAIK no support for anything larger/newer.
I have no hands-on experience with them, but I know the 720KB (Or rather 800KB) 3.5in floppy was what several models of Macintosh used for quite a while during the 80s. In fact, IIRC the first couple models even used 400KB 3.5in floppies.
So, basically, aside from on the Mac side, 720KB 3.5in floppies was common/the norm from when the 3.5in disks were first introduced through about ~1987 or so I would estimate, while 360KB 5.25in floppies (Or 180KB if the drive was only single-sided) were common ~1979-1985 or so. Of course, none of these are firm cutoff dates as I've demonstrated above, more of a broad "most commonly used" time period based on my observations. I'm sure others with significantly more vintage computing experience than me could give more accurate timelines.