we are planning to take train from Venice to Rome, must be on a specific day, in October. Is it necessary to reserve, or can one just show up at the station? grazie!

I think it depends onthe Type of train you go on
http://www.trenitalia.com/en/index.html

Whether trains are busy depends more on the time of day and the day of the week, rather than the month.
You will always be able to get from Venezia to Roma, but if the through trains are fully booked, you might have to get a slower train or change trains. On the vast majority of trains, you can buy a ticket and get on the next train, but if it's busy, you may have to stand.
If you're travelling at a busy time, you should consider reserving seats the day before, at the station or in a travel agency.

Hi ss,

If you know which train you want, why not buy your rickets online at www.trenitalia.com/en/index.html and get it out of the way?

You can't buy online more than 60 days iin advance--but you can check current schedules and pricing to begin planning.