The opera, most theatres and orchestras have their own box office. In addition to that there are two main ticket selling services in Finland:
www.ticketmaster.fi (formerly called lippupalvelu) and www.lippu.fi . For most cultural or sports events you can buy a ticket from one or the other depending on who the organiser has made a deal with. Hence, usually tickets to a particular event are sold through one of these services but not both, so if you cannot find what you are looking for in one of them, check the other before giving up.
Their online service is very practical if you are ready to buy the tickets right away. If you want to make a reservation, you have to call a service number which tends to be very pricey, hence, it may be more economical to make the reservation through the actual organiser (e.g. a theatre or orchestra) when possible.
Related articles
Jazz in Helsinki & April Jazz / Pori Jazz festivals