You can take a couple of big bags on board and mostly you can even find space to store them, but you will have no help with getting them on and off the train, porters are (almost) non existent.
As a good rule, nobody should have more luggage than you can walk around with, without help. (I mean, lifting and walking for a few meters at least.)
I have never found any train in Europe that has a luggage service, paid or free, so even when you are willing to pay, you can not get your luggage taken on the same train as you when you travel.
In some countries you could/can send your luggage while you are on an other train, but I have not seen this advertised in a long time, so do not bet on it.
Even luggage carts on the platforms are rare, often there are non.
Most long distance trains have plenty of luggage space, between seat backs, under seats, in racks at the end of the carriage, and sometimes also in racks above your head.
In local trains you may have to sit at the end of the carriage, in the space meant for people traveling with a bike, as there is extra luggage space there.
There is no charge for luggage on the trains, also not if you bring a lot.