I envisioned that during bomb sirens in Israel, people would rush for cover, screaming, in total terror. That didn't happen. I've heard them only twice, both when I was living in Ashkelon (which is only about 10 kilometers from the Gaza Strip.) They sound like a fire alarm that just goes on and on and on, and permeates everywhere. Both times, they were very effective. It took me probably 30 seconds to process that I was hearing the siren, stop what I was doing (cooking one time, on my computer the other), and get into the nearest bomb shelter. The entire time my brain was screaming "Find shelter! Find shelter! Drop everything and find shelter!"
During my first siren, I was cooking breakfast. I decided that turning off my stove was necessary, but that putting on shoes, locking my apartment, and putting on pants (I was wearing boxer shorts) was not. I raced out into the hallway, where the lights flash when the siren is on, and down to the shelter. I arrived completely terrified, and was greeted by all the veteran residents chatting calmly on their cellphones. It was pretty obvious I was new to Ashkelon.
One siren also goes off on Yom HaShoah, and two go off on Yom HaZikaron. These are drastically different than the ones signaling an incoming rocket. They sound different- the ones for Yom HaZikaron and Yom HaShoah change pitch, and are almost calming. They also inspire a different reaction. Everyone stops. Buses park, people get out of their cars, and everyone stands still for the duration of the siren. It's pretty powerful to be walking along a busy street in Jerusalem, and then to just have everything stop. It's not something I'll forget.