During the very first days in Budapest I saw Kontroll. It is a movie about Budapest public transport ticket inspectors. But as it is fictional movie I think it is ok to list my own real life experiences.
Personally I haven't had problems with them but I have been witnessing interesting cases. I have the feeling that they concentrate on easy target such as yellow metro line and Deak tér especially during the tourist season. As tourists do not know or they are too ignorant to read instructions they often end up traveling without a valid ticket.
I use daily tram lines 4 or 6 as they are identical for my travel to work. There seems to be ticket inspections two or three times in a month. Currently monthly pass is 7650 HUF and punishment for traveling without ticket is 2500 HUF if paid on spot in cash - otherwise the fine is 7500. So basically simply keeping 2500 HUF ready in my wallet I could save 1650 HUF monthly even if I would be caught twice. But my employer pays my monthly ticket so I have no interest for such experiment.
But back to inspectors and especially to people traveling without ticket. There seems to be three categories. First one is the nice people who obey the rules but do not use tickets. Instead they trust their luck or they have done some statistics. If they are see inspector they usually exit the tram or if caught they pay the fine without big fuss.
Then there are people who simply refuse to communicate with inspector. These usually young people do not show ticket or their ID and because inspector has no rights of a police or even a security guard he cannot do much unless they are teamed up with police or guards. If they are about to be caught in a metro station they simply walk past controllers as they cannot physically grab them.
Finally, the most interesting people are tourists and foreigners. As they do not how Hungarian and inspectors usually have only very limited language skills it is somewhat awkward situation. For some it is just some play as they understand very well that single ticket has to be punched in the validation machine in the tram. But it is also rather easy to miss ticket validation machine in complex Deak tér station unless you know that place and system already. And that is why inspectors are there.