Google Custom Search of Theological Journals: “Targets over 1,000 Web sites/pages to retrieve full text articles from hundreds of open access journals and other periodicals related to religious studies, scripture studies, systematic theology, practical theology, and cognate disciplines.”
JURN: an academic search engine that allows you to search for free scholarly articles, chapters, theses, and images. Some of the websites (e.g., academia.edu) may require you to create a free account in order to download the full text.
Google Scholar: Contains books, e-books, citations, articles, and more. Articles that have a [PDF] link are freely available.
Free Books in Biblical Studies (Google Doc): Lists a great number of items available online, mostly in PDF format from Google Books. Organized by subject, including categories such as "New Testament and Early Christianity" (page 33).
Christian Classics Ethereal Library: The CCEL is a digital library of hundreds of classic Christian books. This link connects to their advanced search page, where you can search for authors, titles, and look up a word in all of CCEL's Bible dictionaries and encyclopedias, as well as in Scripture.
New Testament Readings at Religion-online: Provides direct links to the full texts of books, chapters, and essays by recognized authorities. Works are categorized by subject, indexed by author and title, and full-text searchable.
Project Gutenberg: The first and largest single collection of free electronic books, or eBooks.
HathiTrust Digital Library. HathiTrust is a partnership of academic & research institutions, offering a collection of millions of titles digitized from libraries around the world. This link brings up search results for books in English with the keywords "New Testament." Click on options in the left-hand box to narrow your search.
The Theological Commons is a digital library of 79,332 open access books and periodicals on theology and religion, including 29,730 volumes from the Princeton Theological Seminary Library. The collection spans the period from -1800 to 1926+ and covers subjects such as Protestantism, History, Catholic Church, Church History, and more. Formats include books, periodicals, theses, and manuscripts in multiple languages. The material can be read online, or downloaded in PDF, or sent to Kindle.
WorldCat - Find books, e-books, book chapters, articles (including free full texts in some cases), theses/dissertations, and more.
Global Digital Library on Theology and Ecumenism - Online digital library of journals, books, and other materials relating to theology, interreligious dialogue, ethics, and ecumenism in World Christianity. Indexes over 120 journals, most of which are published free online. Note: some full-text articles require you to register for a free account.
Directory of Open Access Journals: DOAJ is an online directory that indexes and provides access to quality open access, peer-reviewed journals. Because this site includes journals in all disciplines, your will have to search for the few that have to do with religion. Tip: try including the words "New Testament" or "Gospel" in your search.