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Be sure the check the main Hiking in Europe page for additional information and links.
I hiked the Greek Peleponesus in April 2007 and Crete in May 2007. Mid to late spring is probably the best time of year for hiking in those areas, since summer and early fall are normally very hot and dry, and late fall through early spring are cold and rainy. Another advantage of spring is that there are fewer tourists. Regardless of season, the only other hikers you will encounter will probably be from elsewhere in Europe, since walking is not particularly popular in Greece.
Oreivatein (Greek Mountaineering Society) has overview maps of the major long-distance Greek hiking trails (E4, E6 and O), though you will have to dig deep to find these maps (they keep rearranging the site). Another source of information is www.pezoporia.gr, though this is Greek only. The major long-distance trail is the E4, which runs across the island of Crete, then up through the Peleponesus and finally up through the mainland (Pindos mountains) towards the border with Bulgaria. The E4 is poorly way-marked, but there are now sufficiently good maps available that it is possible to follow the trail without way-marking on the ground (basic GPS receiver is highly adviseable, especially if the maps you are using have GPS grid). So far, I have hiked the Crete and Peleponesus portions of the E4, as described here for Crete, and here for the Peleponesus.
The Mountains of Greece: A Walker's Guide by Tim Salmon (2006 edition), describes a variety of routes in Greece, emphasizing the mainland. I have not hiked in the mainland myself. Because these are high mountains, hiking may be limited to mid to late summer, due to ice in the passes at other times of year.
The best printed maps for Greek hiking are those of Anavasi, which include a superimposed GGRS87 (Greek Geodetic Reference System 1987) grid. If GGRS87 is not listed in your GPS device, then use the following settings (grid describes the transverse mercator projection from latitude-longitude to GGRS87 northing-easting coordinates, datum describes the Molodensky transformation from WGS84 ellipsoid to GGRS87 ellipsoid):
Another good map source is Omnimap.
[Update as of 2013: Now that almost everyone has a GPS-enabled smartphone or dedicated mapping GPS receiver, navigating with GPX tracks and digital maps is probably a better solution than paper maps. More on GPS here.]
[Update as of 2014: Anavasi is now selling digital maps of Greece, which can be used on the Etrex 20 GPS receiver as well as Iphone/Android.]
[Update as of 2014: Pegasus Maps offers free digital maps of Greece suitable for use on Etrex 20 GPS receiver. I combined routable and contour maps (using GMAPTool) and then downloaded to my Etrex 20. These appear to be good maps.]
[Update as of 2015: TopoNavigator offers digital maps of Greece suitable for use on a variety of mapping GPS receivers, including the Etrex 20. According to the website, these maps include hiking paths, so presumably the E4 and E6 are included. I haven't yet tried these maps.]
The E4 trail continues on the island country of Cyprus, where it runs 539km through the central mountains, from Larnaka to Pafos. I have not hiked in Cyprus myself. English is supposedly universally spoken in the Greek part of Cyprus. More information here:
There are few organized campgrounds in Greece and those that do exist are designed for car campers rather than hikers (rocky ground instead of grass), so I prefer to stay in hotels or wild camp. Budget hotels in small towns typically charged 20€ for a single room in 2007, though sometimes I paid twice this.
English is widely spoken in the tourist areas in Greece, but not that widely spoken in the mountains, so learning basic Greek is highly advisable.
Orthodox Easter is a major holiday in Greece and most people get two weeks vacation then, one before and one after Easter, so that hotels might be booked solid, though otherwise spring is not a busy season in most of rural Greece. Note that the Orthodox Easter often occurs at a different date from the Western Easter. Other potential busy times are the summer season, especially July and August, and the harvest season in early autumn, when people in the cities return to their ancestral villages for a festival. Finally, many hotels shut down for the winter. All things considered, it is best to be prepared to camp.