This databases focuses on topics from an alternative press standpoint:

Alt-Press Watch

Newspapers, magazines, and journals of the alternative and independent press.

These databases cover many topics, including GLBTQ:

ProQuest

Full-text articles, citations and abstracts covering all subjects.

Wilson OmniFile Fulltext

Full-text articles, citations and abstracts covering all subjects.

Opposing Viewpoints Resource Center
(via GaleNet)

Full-text "pro" and "con" essays and articles on controversial social issues.

CQ Researcher

CQ Researcher provides overviews and analyses of current issues.

These two databases have full text newspaper articles:

LexisNexis Academic

Hundreds of regional, national, and international newspapers; business publications, and much more.

ProQuest Newspapers

Nine national newspapers including the Los Angeles Times and Wall Street Journal.

These databases have articles on GLBTQ topics, but from various disciplinary perspectives:

ABI / Inform
(via ProQuest)

Full-text articles, abstracts and citations to publications covering business, management, and economics. Includes full-text of the Wall Street Journal from 1984.

EconLit
(via Cambridge Scientific Abstracts)

Citations to publications covering all topics in the field of economics.

Historical Abstracts
(via EBSCOhost)

Citations and abstracts for publications covering world history (excluding the U.S. and Canada).

Literature Resource Center

Biographies, bibliographies, and critical analyses of authors from every age and literary discipline.

MLA International Bibliography

Citations from scholarly publications on literature, language, linguistics, and folklore.

PsycINFO
(via EBSCOhost)

Citations and abstracts from nearly 2000 publications in the field of psychology and the psychological aspects of related disciplines.

Sociological Abstracts
(via Cambridge Scientific Abstracts)

Citations and abstracts of publications in sociology and related disciplines.

Worldwide Political Science Abstracts
(via Cambridge Scientific Abstracts)

Citations and abstracts to political science literature, 1975 to present.