"if wire is plugged into a breadbord, the electrical path in it is surrounded by plastic"
Mechanically that may be true, electrically the wire is still connected to the microcontoller at one end, and nothing to the other end.
You want to make sure the wire has valid voltage on it. One way is to use the internal pullup resistors that retrolefty brings up. There are no internal pulldown resistors.
void setup() {
Serial.begin(9600);
pinMode(2, INPUT);
digitalWrite (2, HIGH); // connects internal pullup resistor - digitalRead of 2 returns HIGH, or 1, unless pin is pulled low, then it returns LOW, or 0.
// if using IDE 1.0.1, this does the same
pinMode(2, INPUT_PULLUP);