How many PIR Motion Sensors can I connect to my Arduino-Uno R3?
Most PIR sensors provide a simple relay output. That means they are nothing more than a switch as far as the Arduino is concerned.

You can connect hundreds of switches to an Arduino. With judicious use of diodes and a matrix arrangement you can hundreds with not many IO pins.  For example an 8x8 matrix of switches gives you 64 PIR sensors with just 16 IO pins.  For n pins you can have (n/2)² switches with a balanced (n/2 by n/2) matrix.