When researching train connections between Rothenburg - Interlaken, Interlaken - Venice, La Spezia - Rome, I have found that www.raileurope.com has the most options.

Has anyone had experience with the site? It offers many more options than bahn.de, trenitalia.com, or sbb.ch. Is there a catch?

Thanks

Yes, it is as a rule significantly more expensive as they add fees to every ticket and often do not show any of the special fares available for point to point tickets.

Yes, there is a catch. You'll pay substantially more for your tickets through raileurope than the other websites you listed.

I have trouble believing that the RailEurope site (and BTW, the prices on that site are not ALWAYS more expensive but I'd only use them as a very last resort) has more options than the GermanRail site..in fact unless I am mistaking your use of the term "options" there is NO WAY the germanRasil site isn't more complete in terms of listing timings, etc.

Many more options in what sense?
Normally, the Deutsche Bahn and SBB sites show comprehensive timetables not linked to whether trains can be booked or not.
If trains need to be booked (and most don't), then that is best done through the national rail website of the appropriate country.

Between the examples I gave, would I be safe just showing up and not booking in advance?

I do have a couple hotels booked so I will need to be arriving to each city on our planned day.

Long distance trains to and within Italy require a reservation. For those legs, buy a ticket at any station a few days in advance.
For trips within Germany or Switzerland no "booking" is required.

RailEurope is a reseller of train tickets and there is no way they could offer more routes/departures than the individual countries that operate the rail systems. It's like buying plane tickets from Expedia instead of directly with the airline except RailEurope has a much bigger markup fee. RailEurope is also listing tickets/schedules that may not be available yet as some countries only list schedules 60-90 days at a time.

You can not purchase an international ticket on Trenitalia unless you are picking the ticket up in Italy.

Here is a list of European train companies (not resellers) with links to their websites.
http://www.ccl.kuleuven.be/~corn/railinfo.html

Part of your route in Italy (La Spezia) may be on a slow train that doesn't allow seat reservations. The fastest trains (AV, ES, ICPlus) in Italy are only on certain routes.