Due to the many daily bus and rail services between Denmark and Sweden you cross the Øresund Bridge even if you do not have a car. Here is an overview.
DSB - responsible for the Øresund trains from Denmark
www.dsb.dk

Skånetrafiken - responsible for the Øresund trains from Sweden
www.skanetrafiken.se

SJ - operates the trains between Copenhagen and Gothenburg/Stockholm
www.sj.se
Gråhundbus operates the routes
Copenhagen - Ystad - Rønne (866)
Copenhagen - Malmö (999)
www.graahundbus.dk

Go By Bus (formerly Säfflebussen) operates the routes
Copenhagen - Gothenburg - Karlstad - Stockholm (100)
Copenhagen - Gothenburg - Oslo (300)
www.gobybus.se

Eurolines operates the routes
Copenhagen - Stockholm
Stockholm - Munich
Oslo - Frankfurt
www.eurolines.se

SwebusExpress operates the routes
Copenhagen - Malmö - Helsingborg - Jönköping - Linköping - Stockholm (832)
Copenhagen - Malmö - Helsingborg - Halmstad - Gothenburg - Oslo (820)
Malmö - Copenhagen - Hamburg / Berlin (901/902)
Copenhagen/Kastrup/Malmö to Kristianstad - Sölvesborg - Karlshamn - Ronneby - Karlskrona - Kalmar (834/820)
www.swebusexpress.se