General Brazilian
perder a consciência / desmaiar
Most common; 'desmaiar' is also widely used for fainting
Rio de Janeiro
apagar / perder os sentidos
Informal usage; 'apagar' means to black out
São Paulo
perder a consciência / cair desmaiado
Standard usage; 'cair desmaiado' emphasizes the falling aspect
Portugal
perder a consciência / desmaiar
Standard European Portuguese; same as Brazilian in this case