Should smoke detectors be on AFCI/GFCI breakers?
AFCI is required, but not GFCI, modulo local amendments
Assuming that your jurisdiction doesn't amend this, the requirements for smoke detectors/alarms in bedrooms (NFPA 72, NFPA 101, IRC/IBC) overlap with the AFCI requirement for bedroom outlets (both receptacles and lighting outlets) to force the smoke alarms onto an AFCI protected circuit under all recent NEC editions.
There are two ways I've seen to deal with this: either you can put in a residential alarm system with system smoke/CO detectors (and get the brains of a burglar alarm from the deal), which means you get to take advantage of the 760.41(B) requirement that fire alarm panels not be on AFCI or GFCI, or you put the smokes on the same circuit as frequently used lighting loads, so that breaker trips are troubleshot promptly.
As an aside, NFPA 72 29.9.4 point 5 requires smoke alarms that are AFCI or GFCI protected to have battery backup power.  If the 7 days of standby + 4 minutes of alarm backup power requirement given for dual-powered smoke alarms is insufficient, such as if you're dealing with a &quot;snowbird&quot; situation in Florida, then it's best to go to an alarm panel.  (You'd probably want the alarm panel anyway, as local smoke alarms are going to do you no good when it's July and the house is vacant and neighborless to begin with!)