JSTOR provides full-text access to the archives of core scholarly journals in the arts, humanities, social sciences and sciences. Its coverage of psychology is fairly light (only 14 titles) but it is fairly strong in sociology and feminist & gender studies.
Dates of coverage vary by journal title. All go back to the very first issue published, but most have a "moving wall" embargo that excludes issues from the most recent X years (where X can be anywhere from 0 up to 10 years, depending on the particular journal; most are in the 3 to 5 year embargo range).
JSTOR now also includes the full text of current issues (up to the latest issue) for selected journals from selected publishers, including the University of Chicago Press.