You can read or download the last three years of Palestine Exploration Quarterly for free with a simple registration, for a limited time. You can see the table of contents here. The issues from 2009-2011 appear to be free without registration from the table of contents. Here are a few recent articles that caught my eye:
The Location of Tarichaea: North or South of Tiberias?, by Nikos Kokkinos.
The Protestant Garden Tomb in Jerusalem, Englishwomen, and a Land Transaction in Late Ottoman Palestine, by Ruth Kark and Seth J. Frantzman.
Members of the Palestine Exploration Fund receive four issues of PEQ a year (as of 2013) as well as other privileges.
UPDATE (11/10): They changed the free access noted above. You should still be able to get to the content by registering for their free and informative mailing list.