I am writing this question in the train from Roosendaal to Leiden. The train provides a decent wireless internet connection. I have seen it before, but then it was an experiment on trains between Rotterdam and Utrecht with very wonky connections. Are the wireless connections now common on all trains and if not how can you know which train has wireless internet?
From the website of the largest traincompany, NS
Basically, you will find free (!) Wifi in certain Intercities (the quick trains between different cities) only. These trains are not specified on beforehand, but you can recognize these trains from the Wifi-logo on the outside of the train. You have to connect with the "Wifi in de trein"-network.
For now, the usage of the Wifi is free, but if I remember correctly they are mainly performing tests at the moment, so certainly not all trains are equipped with the free Wifi.
I expect it to become a paid service when it is fully operational on all trains, but I do not have a source for that.