Esbjerg has a direct line to Copenhagen (around 3 hours journey) with trains every three hours or so daytime, and there are also several trains to Arhus. Changing at nearby Bramming, you can also get to historic Ribe easily.
Ferries sail to Esbjerg from Harwich in England at least twice a week. At the moment, the DFDS Scandinavian Seaways use the "Dana Sirena" which is a freight liner renovated to also suite a small amount of passengers and this makes it quite a relaxed crossing as you have just enough to make the 17 hour crossing comfortable - a couple of restaurants, a bar, a cafe, small shop, kids playroom and a deck bar, whilst having none of the rowdyness of bigger ferries with discos and lots of parties going on. Cabins come for between 2-6 people and several have TV apart from being en suite. I certainly hope to use it more frequently. Some years ago, I took the Gothenburg to Harwich and then Newcastle ferry, run by the same company until it was discontinued in 2006, but in fact I prefer this route now that I am in the south of Sweden, especially since it cuts travel time by nearly six hours as you are already by the North Sea coast when you start off in Denmark.
By car. The town should be within easy reach from most places in central mainland Denmark or even northern Germany, but of course it's quite a long way away if you happen to be in Copenhagen ...
On a bike. But beware - as far as I know there's only one place in Esbjerg where you can rent a bike, so better bring your own! (Where to rent a bike? According to us, this is the only place to rent one: Skraentens Cykelwerksted, Villy Hundrup, Hj. Skraenten/Kirkegade 6700 Esbjerg tel.: 75-457505)