It's cheap, fast, clean, on time, scenic, relaxing, you can make new friends, not worry about excess baggage or extra carryon luggage. There are no checkin queues or hassles and you're not confined to your seat. You can bring your own food on board without feeling conspicuous or there are rolling drink and food carts that go through each train wagon. There are also restaurant / bar wagons on long-haul trips.
My father took me on my first rail adventure through Europe when I was 9 years old and it opened my eyes to rail travel ... I haven't looked back since and have travelled with friends, family and recently with elderly parents without any glitches what-so-ever.
I've always booked through Eurail and depending on the deal you choose, Eurail has packages that offer unlimited travel over a block period of time. The only constraint is when you're 26 + years old you don't have a choice in the class of travel ... but when you reach that age, surely 1st class travel is the only choice of travel !!!
A recent trip to Europe with my elderly parents, I had booked first class travel from Prague to Austria. The particular train we were booked on didn't have a first class service, so even though we booked on first class, we had to sit in economy / second class. There was no booking mix up it was the particular route which didn't have first class service. The train attendant explained the situation and told us to contact Eurail for a refund. I did this and sure enough Eurail refunded the difference between 1st and 2nd class.
The added benefits of booking a Eurail pass - there are some ferry trips included in this and there are discounted entry fees to museums etc ...
I've also travelled on cheap flights and the angst just isn't worth it.
I guess I'm still finding it hard to get used to the fact that Europe now encompasses a whole lot more countries than it used it. I still think of Europe as France, Italy, Spain, Germany, and Nordic countries, which you can travel to by boat.
Definitely Eurail as you can buy this before you leave Australia, and it is relatively cheap this way.
All European towns have great train services, both fast and slow, and the system connects to so many places that unless you are driving, I would not bother going by plane.
Even on long trips, if you get a sleeper, it is still fun and exciting and not the hassles of a plane unless you get on the wrong carriage, which we have done a few times when we first used Eurail, and ended up in the wrong city as the trains change in the night -i.e. they are all marked and some get shunted off at night to go in other directions so it is important that you get on the right carriage.
Great way to travel as their trains are comfortable and interesting to meet locals and tourists.
I think it depends on whether you see the journey as part of the experience. Flying gets you to the different places much quicker, so you have more time to look around when you are there, and it can be very cheap as well. Probably cheaper than train travel in many cases.
But there is still something special about train travel - watching the landscape flash by and seeing how it changes as you go from urban to rural and from country to country. French and German trains are very fast and efficient, I couldn't recommend British or Belgian ones though!