Zealand

By train
By train

The vast majority of regional transportation is done by train, the bulk of it on the 4 main DSB (http://www.dsb.dk) corridors, radiating out of Copenhagen. It is worth noting that that the ticketing system changes in Borup and Hvalsø, roughly half way between Roskilde and Holbæk & Ringsted respectively, if you cross these cities "All-Zone" tickets bought in Copenhagen are no longer valid, and you need to purchase train tickets with DSB instead,

North
Copenhagen-Elsinore
West
Copenhagen-Holbæk-Kalundborg
South-West
Copenhagen-Ringsted-Korsør
South
Copenhagen-Ringsted-Nykøbing Falster
By bus
By bus

The regional transportation agency for the whole region is Movia (http://www.movia.dk). Though the lionsshare of long distance transportation in the region are done by train, there are a few important interregional routes namely:

60
Vordingborg - Maribo Lolland
62
Vordingborg - Stege Møn
64
Vordingborg - Bogø - Stege Møn

And two mainly summer express buses (http://www.hurtigbussen.dk) which non-stop between Høje Taastrup and the beaches and vacation homes in North-Eastern Zealand:

555
Høje Taastrup - Holbæk - Odden ferry to Jutland
666
Høje Taastrup - Nykøbing Sjælland - Rørvig ferry to Hundested
By ship
By ship

The most important ferry route on Zealand is between Hundested and Rørvig (http://www.hundested-roer...), crossing the big fjord in northern part of the island. Many of the smaller islands dotting the sea around Zealand and Lolland are also connected by ferries, check these in the relevant sub regions,