I'm planning to go away this summer for just a month and i'm trying to fit in about 8 countries travelling via train. I wouldn't worry about not seeing everything, just see whats most important for you.
Some people have said to me and my friends that we wont see a lot and will always be travelling if we try to fit it all in but the way I see it, at a young age (18) I will only want to see the main sights in each place anyway then go on to the next place. If I wanted to slow it down, relax all day and spend ages in one place, I would go on a normal holiday - not tour around Europe.
Hope you have a good trip
If you wizz through loads of countries ticking off boxes of sights as you go then yes, you will see things. But you wont really see the countries you are in. You wont have any idea whatsoever about the atmosphere or the feel of a place. But if seeing as much as possible to tell your friends how many countries you have been to then yes by all means, wizz round as many as you can (you can even go round the UK and say you have been to 4 different countries, when really it is only 1!!!)
It all depends on how much you want to see. I went to five countries in three weeks; staying a max of 3 days in each. The days were action packed, but it was definitely worth it! I'd say it's possible if you stay within one region (E.g. spain-greece), but if you try and hop up to Poland and Denmark it might make it tricky.
I agree with both the interrail people and the two country people!
It's up to you what you mean when you say 'see' a country. If you want to get a quick feel for the place go for it, city hopping and hopefully meeting a local or two. The longer you spend somewhere the more you'll get to know.
Ideally you want to spend a month in every country but that's the dream, eh?!
I did the interrail 11 countries in a month thing and thoroughly enjoyed it. As a result I have moved twice to countries I visitied on that whirlwind trip both to work and because I liked them initially.
That said, are you flexible? If you plan to visit all those countries (though I think some of the distances might be a hassle - Greece for example, Athens is quite a treck!) and you decide you love, Poland, you can change your plans and just stay there.
If you want any country specific advice I spent some time (i.e more than 4 days!) in Germany so I can help there
Best of luck!!!