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Rostock is a city in the north-east of Germany.
South towards Berlin,
Take bus number 23 from the central station in Rostock. Go out at exit Brinckmansdorf. There is be a Total petrol station 200 meters in the direction of travel. About 400 meters further is a big intersection, with a right turn leading to the A20 south. You have several good options: 1) Ask drivers at the gas station if they're going your way. 2) Go to the traffic light and turn left. There is a space for cars to stop on the onramp. 3) Hitch just before the gas station entrance, so cars wanting to stop just turn into it. There's a traffic light so the cars will be somewhat slow.
Advices for signs: ss there are many cars not going very far, write a sign with "Güstrow" and let them drop you off at the gas station right before the exit of Güstrow. There you an easily find cars going to Berlin or even further.
Take tram 2 or 5 to Südblick (the last stop). Walk in the direction of the tram out of the city. There is a good hitching spot at the bus stop about 200 meters from the tram stop. Bring a sign that says 'A20 ost' or 'A20 west'.
You can also follow the directions above and try to hitch with people taking the A19 to the A20, but only accept rides from people taking the A20 because it is impossible to stop at the intersection.
You can get to the port by taking the Shuttlebus 40 from the main station or Kröpeliner Tor to “Rostock Fähre”. This Shuttlebus will cost EUR 2.50 more than a normal ticket.
Alternatively take the train S1 (towards “Warnemünde”) to station “Lütten Klein” and change to bus 45 to “Seehafen Fähre”. It won't take much more time and you don't have to pay an additional fee.
Check timetables here.
North towards Denmark
The ferries leave every two hours, along with Bus 40. Just follow the signs for the ferry to Gedser. It´s probably best to ask the cars queueing in front of the ticket booths, or before they buy them at the ticket offices. Drivers pay for their car regardless of the amount of passengers, and they can add passengers to their ticket at the booths. The queues are much shorter in the winter so it´s harder to speak to the drivers before they get to the booths. If you´re going to Copenhagen you can also hitch to Sweden, Trelleborg, then across across through Malmo into Copehagen. These ferries go less often and have longer queues for hitching, but the journey takes several hours. If no one picks you up, the passenger fee of EUR 7.50 is reasonable. As a pedestrian you have to catch the pedestrian-passengers-bus 30min before departure, so be there on time. On the 1hr 45min trip, you can ask other drivers if they are going in your direction. It's really easy to get a ride to Copenhagen.
Update 2018: I asked the staff in Rostock (for the line HRO - Gedser) and they confirmed: per vehicle are 9 free persons included. Drivers need to say how many passengers there are, but there is NO extra fee for hitchhikers/extra passengers. Even if the ticket is bought in advance, it's little to no effort to change the passenger amount. Plus the ticket sellers said it's okay to hitchhike, but not directly in front of the ticket booths.
You can ask stuffg at the ticket booths to Trelleborg if they can add a free passanger in car
If you don't find anyone to hitchhike with, the student fare with TT Line to Trelleborg is currently (27th March 2013) 16 € (but 32 € regular!), Stena charges 26 € for everyone. You need to be there 30 minutes before departure.
The ferries to Helsinki apparently charge based on the number of passengers, but maybe you can make a deal with a driver.
The ticket sales place in the ferry port is open 24 hours and they let you sleep there.
One can find a quiet corner to sleep in the train station too, but the police seem to always check your papers in the night. People piss a lot around the station but you can find clean spots too.