Any number of books and tv shows on the subject generally highlight the frustrations and joys of this kind of adventure.
Suggest you stay a while in your chosen location in a friendly hotel, talk to other expats, and "test the waters" in all seasons, particularly the heat of summer and the cold of winter.
Good luck... and keep us posted, maybe through a blog?

Almost every island has an agency where you can arrange to rent a property for an extended period. If that period includes the summer months you will be expected to pay full price during those months, but off-season rent will be reasonable, as the property would likely sit vacant anyway.

If you wish to stay over winter, pick an island with a large enough permanent population to sustain off-season activities and businesses, or you will feel very isolated.

It's important to know what time of year you wish to stay, and which island(s) interest you. Also, do you have the right to stay in Schengen beyond the 90 days in 180?

Crete: google air b n b, Chania Seaview, a very nice property, walking distance to historic center.
Also, a good agency is www.dikynna-travel.gr, contact Maria.
Only a 90 day stay allowed in a Schengen country without an extended visa.

Best way to find a long term rental apartment or house is to contact a local real estate agency.

Travel agencies have no access to these kind of rentals, but only to apartments and houses that are being rented on a daily basis.

Renting an apartment in a place that attracts tourists can cost quite much, especially if the rental period includes the high season months.

I have rented apartments on islands such as Lesbos, Santorini, Crete etc, it was always easy to find them at the beginning of the season.

Clausar is correct, and the agencies to which I referred in my first post are indeed real estate, which handle both long-term rentals and property sales. This is an example from the island I am most familiar with: http://www.anael.gr/forrent.htm

I'm not suggesting Antiparos for you, as the island gets very quiet off-season. If you are planning to stay during winter, Crete would be the most logical choice among the islands. Were it me looking for somewhere to stay over winter, I would choose somewhere on the mainland, perhaps southern Peloponnese.

Golfernz1, your screen name suggests you are a Kiwi. Do you also have a Greek passport or one from another Schengen country? If not you may find it difficult to legally stay in Greece for more than 90 days.

Thanks for the replies and to elaborate on my experience. I have been to Greece before and to Crete plus six other islands so I'm quite familiar with the area. Yes, I have googled many long term rental sites and picked out my favourite ones to date. As for Schengen whatever, I had no idea what you were talking about and googled that. By the time I wish to do this I will be retired and my country has a reciprocal agreement with eight other countries for living or staying over the 90 day limit. That's just for retirees by the way.
As for visas, there are very few countries that I need a visa for up to the three month limit as at the present time.
Thanks for the website suggestions, I'll follow that up now.

I Know of a flat on the island of Spetses. The owners are looking to rent it out for more than 3 months at a very reasonable price for the island. This is the website with pictures etc. If you are interested send them an e-mail.
Spetses is a fantastic island, very beautiful. Good Luck!!

FOrgot to give you the link!! www.astero-apartment.com

Just a side note:
Make sure that whatever apartment you consider, have proper heating installation for winter. Many apartments on the islands were originally built only for summer use, so they only feature air condition (if so!) . This is not the best way to get warm on winter, especially giver the humidity on the islands and the poor insulation most of those buildings have. After putting air con on heat mode and reaching an acceptable temperature,switching off for a couple of hours, all heating will go away. Not to mention soar throats etc resulting of long air con use. Even if you are alright with this, electricity bill using an air con all day long will reach the sky ! Although fuel cost is very expensive, radiators are the best and more reasonable way to keep warm on my opinion.