Just a quick disclaimer: these experiences and opinions are all of my own from taking public transportation throughout my stay in Israel. Different people have different experiences, but some of these are relatable for many so I thought to address them. Happy traveling!
1. Road rage
This is specifically applicable to the bus drivers and 95% of drivers in Israel in general. Rights (not necessarily rules) on the road are taken very seriously, so if anyone is in the way of another for approximately five seconds, you're bound to hear honking. While taking a bus in Tel Aviv, the bus driver repeatedly honked at drivers cutting him off. Understandable and relatable, but there are probably better solutions than getting angry.
2. Loud phone calls
In places like Japan, people are not allowed to make phone calls on public transportation in order not to bother anyone. So the trains and buses there tend to stay super quiet. In Israel, you're basically allowed to call whoever you want, whenever you want. It's normal to hear people having long, loud conversations on their phones. And you can't do much about it no matter how much you want it to be quiet, unfortunately.
3. Free-for-all newspapers
In the morning, many people read the newspaper on the train on their way to school, work, etc. There are usually newspapers available by the entrance of every station. Consequently, people usually take and read the paper, then leave them on the floor or tables of the train for others to freely grab and read. I've encountered people arguing over who had possession over the paper, who grabbed it first, and so on. People need to know what's going on in the country some way or another.
4. Sleepy soldiers
Since there are a lot of younger soldiers serving here, it's common to see them taking the public transportation in the late afternoon when it's time to go home. Just like any other person after a long day of school or work, soldiers are tired too. Many fall asleep and some even accidentally miss their stops or wake up in confusion. Once I was riding the train home when the train arrived at a station. The soldier sitting in front of me woke up suddenly, realizing the train had made a stop. He grabbed his belongings and got off the train in a hurry. I guess he realized outside that he had gotten off at the wrong stop, but it was too late; the train had already started to move. It was definitely a moment of pity.
5. A lot of conversing and standing up in general
It's a cultural thing for Israelis to talk to one another, even to strangers, about essentially anything on the spectrum. So whether you're on the train, bus, or airplane, you'll notice that people like to get up and walk around to converse with others especially during crowded rush hours, whether they're friends or strangers. As opposed to the quiet trains of Japan, Israel's trains are pretty lively, to say the least.
6. Delays and malfunctions
This is specifically about the trains which occasionally experience some mess ups and delays. Sometimes the automated announcements are totally off, so the people in charge physically have to make the announcements of the next stops in order to avoid confusion. Sometimes the train may stop randomly because it's arriving too early to a station. The possibilities are endless for delays.
7. As much aggressiveness as friendliness (& beautiful scenery)
Taking public transportation is a great way to get around from place to place conveniently and inexpensively. In Israel, you'll experience many moments of aggression and loudness as well as the welcoming attitude and friendliness of the people. And depending on the road, you might see some amazing views from your window.