Trains in the Cinque Terre

There are trains that go directly from Rapallo to Vernazza: a lot of regional trains from (Savona-)Genova to La Spezia.

For example, you can take the Regionale 11291 (Timetable http://www.e656.net/orario/treno/11291.html) that leaves Rapallo at 14:07 and reach Vernazza at 15:20.

Trenitalia tries to sell fast trains because you save about 15 min but you have to change.

Regional train tickets are also sold on the Trenitalia.com website but you can buy the ticket in the ticket office just a few minutes before the train leaves, and the price is the same! (In Rapallo there should be a ticket office, in Vernazza I don't think there is). But you can't book a specific seat, if the train is crowded then it is possible to travel standing on foot.

You can download the official Trenitalia Timetable from this address: http://www.trenitalia.com/cms-file/allegati/trenitalia_2014/informazioni/orario_digitale/Tuttitalia_light1305.pdf

In this PDF the Genova-La Spezia line is listed from page 269 (Section 31). It is valid till June 10th 2017.

Trenitalia says that to get from Rapallo to Vernazza, you have to change at Levanto

Primarily because most long distance trains stop at Monterosso and probably Riomaggiore and not necessarily at the other villages. Hence they are asking you to change and take one of the local trains(treno regionale) to Vernazza.

When I was taking the train from Vernazza to Monterosso, I saw many trains which didn't have a stop at Vernazza in both directions.

Even more annoyingly to get back to Genoa from Vernazza, you have to go via La Spezia

Don't think so, I just checked up timings on Trenitalia and it says change at Sestri Levante/Levanto and onto Genoa.

I am assuming you are looking for trains for the whole day and not at specific times.

It heavily depends on the day of the week you are looking at, some trains passing by 5 Terre are suspended during weekends and holidays because, hey, it's the period they are most needed...welcome to Italy!

So, for example, the Regionale 11291 suggested by Enrico is not operating on Saturdays and Sundays.

On top of that take into account that in June the timetables will change, and it's not granted that Trenitalia website will be fully sync'd to the real timetables for a few days.

My suggestions:

• search on the site for the exact day you plan to go, otherwise you could get some nasty surprise.
• if you plan to travel after 14/07/2017, wait a few days after that date to check for the new timing table
• never ever trust any site other than the official one, and use only the home page timetable search. Official time tables can and are changed frequently according to maintenance works on the lines, and maintenances are not planned a year in advance so to have officially printed or pdf-ed timetables always be updated (and this is normal for almost any train company). So if you resort to some third party website or a pdf, you run a good risk to rely on an obsolete information. The good news is that Trenitalia site was a scam 'till some months ago tricking tourists to buy highly expensive tickets, but after a few years of complains it's been finally fixed and now you don't run that risk anymore, so use it :-)

A small update, as I was reading the other answers again: do not rely on ticket offices. They can be totally missing, they can be present and closed, and they can be present with only the automatic machine, which is more often than not broken or not getting card when you don't have coins or not getting coins when you have only them. As tickets last for 24 hours, always buy in the morning all the tickets you need during the day at either La Spezia or Genova.