The best way to explore Corfu is to rent a scooter. There are of course also bus connections, but it's so much more fun being able to stop wherever you want and not having to wait for the busses. Besides, Corfu is a hilly island with often steep streets leading down to the beaches; thus it's nice getting on the scooter, instead of having to walk up the hill after a relaxing day on the beach. We rented a scooter the whole week, and made daily trips around the island to different beaches, small mountain villages, Corfu town etc. I guess a car would be good as well, but with a scooter the parking is less of a hassle. The main roads along the coasts are in very good condition, the smaller inland roads in less good shape, but they are also not as busy as the main roads.
Just like on most other Greek islands, also on Corfu there are shops/stands in every bigger resort, where one can rent scooters/motorbikes. Many of the hotels also rent out their own ones. My experience is that the prices don't vary that much, but it can still be worth looking around for a good deal, especially if you're planning to rent the scooter for more than a couple of days. The longer you rent it, the cheaper the daily rate will be. Just remember to buy a good map of Corfu, and off you go! Have fun!
Corfu is probably the greek island with the best roads, which are brand new and lead everywhere...This would be a great Idea to take your car on the ferry if you come from Italy, cause it will be useful.
There is also a great bus system in Corfu, with many busses going everywhere...
From Corfu town you have the main line #7 bus ( blue bus) going up north for Gouvia, Ipsos, Pirgi, Dassia.
And the green busses going everywhere for really cheap...
But you won't be alone in these buses..
The most easy way to travel is to rent a scooter but watch out for greek scoot riders...not really careful... ;o)
In summer 2007 prices were (per day + gasoline):
Kia Picanto - 30e per day
Daewoo Matiz - 25e per
Small cars, but ideal for 4 person transportation on the tight island roads.