Estonia has connections with many countries by the Baltic Sea, with very nice and calm boat trips to many cities (sometimes a little rough and bumpy in autumn). You can bring also your car or motorcycle, if you would like to drive around Estonia (many Finnish come with their motor-homes).
Tallinn Port (Tallinna Sadam) is located quite in the city center, with a beautiful view to the Old Town. In their website you can find more information about ferry companies and timetables. Usually, you can book and buy tickets for ferries in their company websites or in travel agencies all around Estonia.
Estonian company that operates ferries between Estonia, Finland, Sweden, Latvia and Germany. Unfortunately, website only in Estonian language, but there you can book the tickets and find discounts and season-offers, which are great (like a day-cruise from Tallinn to Stockholm for 500 eek). But you can always go to their office or call and talk in English.
A Finnish company that has ferries between Tallinn and Helsinki, part of a bigger network that offers 5 Ferry routes to Estonia from Sweden, Finland, Germany and Russia. Website in English and Estonian.
A smaller Finnish company that has ferries between Tallinn and Helsinki, and cheaper prices (my local friends who travel frequently to Finland usually take this one). Website in English and Estonian.