One of the worst affected areas is Ceredigion, along the A487 coast road between Cardigan and Aberystwyth.
The Mid and West service says crews are on their way to rescue four elderly people stuck in a car on the Gwbert Road, Cardigan.
At 20:30 GMT on Thursday, Natural Resources Wales had issued three flood warnings and many flood alerts.
About 15 to 20 homes have been flooded around the Ceredigion coast road. Fire crews from New Quay, Aberaeron, Aberystwyth, Lampeter and Tregaron are all dealing with incidents.
Just before 19:00 GMT, firefighters had to rescue another group from a vehicle at Cennarth Bridge, Newcastle Emlyn.
Meanwhile, South Wales Fire and Rescue Service says it has also been dealing with flooding incidents.
A crew has rescued a female driver trapped in a car in flood water at Pontsarn, Bridgend.
Firefighters are also dealing with flooding close to properties at Harriet Street, Trecynon, and clearing flood water at Ash Street in Abercwmboi, in Rhondda Cynon Taff.
Crews in North Wales have received reports of flooding in Gwynedd, but say the incidents have been passed on to the council to deal with.
Earlier today, rail commuters were warned routes could close at short notice over the weekend due to potential flooding.
A yellow "be aware" weather warning for rain has been in force all day, and in place until 21:00 on Thursday.
Firefighters across Wales say they are dealing with flooding incidents, after days of torrential rain.