I plan on going to europe from May 14 to June 13th, My plane would arrive in Paris and I would Depart in Rome. Here is the itinerary I was looking at:
Paris- 5d
Brussels-2d
Amsterdam-2d
Munich- 2d
Verona-2d
Venice-2d
Florence-2d
Rome- 4d

Train travel- 4.5 days
Airports- 2 days

Do you guys think this itinerary is possible? I'll be staying in hostels and cheap hotels i really don't mind as long as I can see Europe, how much money do you guys think is needed per day? I plan on buying a Eurail pass for trains. Its 30 days and so far I have 9 days left, should I add them to the cities already there or should I see other cities?

It's possible. I would drop Verona and possibly Brussels to ease up on the travel.

oops not 9 days 3.5 ish depending on train travel.

Your reason for Verona is? Unless you are planning on one of the opera performances which are unequaled in many ways, I do not think you would otherwise need two full days there.

You realize you are doing a certain amount of backtracking although you could take a night train service to Munich or you could skip Munich entirely.

I would add a day to Venice and a day to Florence IF you plan to skip Verona.

The problem is we have no idea what your interests are. Depending on those there are SEVERAL places IMO you could eliminate entirely.

I'd drop Brussels and add Bruges instead, and would drop Munich, as it is taking you too far east for this trip.

You also might want to consider dropping Belgium altogether and taking the train south to Lyon and then to Provence and the Riviera.

I guess you're right about Verona, I don't want to skip Munich though, what i was planning was sort of cities with different architectural styles and food.

Interests:
Architecture
Food
Museums
Sightseeing
Photography

Munich is almost directly north of Venice. I do not see how it is out of the way.

Don't limit your travel options to rail. It is possible to book an inexpensive flight that will save you travel time (and sometimes money), which of course allows more time for sightseeing.

I find it helpful to write it down in real time. Is this what you were thinking?

5/14, Day 0. Arrive Paris
5/16, Day 1. Paris
5/17, Day 2. Paris
5/18, Day 3. Paris
5/19, Day 4. Paris
5/20, Day 5. Paris
5/21, Day 6. Train to Brussels (90 minutes)
5/22, Day 7. Brussels
5/23, Day 8. Brussels
5/24, Day 9. Train to Amsterdam (2 hours)
5/25, Day 10. Amsterdam
5/26, Day 11. Amsterdam
5/27, Day 12. Train (7.5 hours) or fly (90 minutes+) to Munich
5/28, Day 13. Munich
5/29, Day 14. Munich
5/30, Day 15. Train to Verona (5.5 hours)
5/31, Day 16. Verona
6/1, Day 17. Verona
6/2, Day 18. Train to Venice (1+ hours)
6/3, Day 19. Venice
6/4, Day 20. Venice
6/5, Day 21. Train to Florence (2+ hours)
6/6, Day 22. Florence
6/7, Day 23. Florence
6/8, Day 24. Train to Rome (90 minutes)
6/9, Day 25. Rome
6/10, Day 26. Rome
6/11, Day 27. Rome
6/12, Day 28. Rome
6/13, Day 29. Fly home

For me, this would be too much moving around, too many hotel changes and too many train stations, but this is your trip.

Skip Brussels and head straight to Amsterdam, giving yourself 6 nights there. There's lots to see and do in Amsterdam, especially for young people, but you could also easily take a day trip to Bruges, Ghent, or many other places.

You might also consider working a non-city destination into your trip. If you are trying to get a nice taste of Europe, much of the continent is made up of non-urban areas. Perhaps some time in the mountains outside of Munich, or the Italian Lake District, French countryside, etc.

If food is one of your major interests, spend time in Belgium and do not spend 6 nights in Amsterdam unless you bring your own food.

If your interests are museums and architecture, going to cities makes a lot of sense. You can see Verona on a daytrip from Venice if you get antsy in Venice.